Very sorry, you guys are correct and my video is wrong. I only present the answer if both A and B are impossible scores to attain. I have put a note in the video.
Unfortunately this whole problem does not work, as there is a rare way to score a single point in American football (occurred only twice in the NCAA and not once since 1940 in NFL) thus you can literally have all positive whole numbers and 0 as scores
You've explained why each number can be attained in a very cumbersome way, once you have 2 and 3 it's obvious that you can reach every even number (just keep adding 2's) and every odd number besides 1 (just start with 3 and keep adding 2's). Therefore you can reach all numbers.
What scores are not possible to get to in an NFL game? That is what I originally wanted to answer but I messed up in the video. A recent NFL rule change also allows for 1 point safeties. If one team scores a touchdown (6 points) and goes for a 1 point conversion but messes up the point-after kick, the team on defense can return that for 1 point--called a 1 point safety. (In the past the play was ruled dead if the defense blocked the kick). So this means a score of 6-1 is possible. Then, since it's possible to get to 6-1, it is also possible to get to 8-1, 9-1, and so on since a team can then increase its score by any number larger than 2 (as shown in the video). The 1 point safety only occurs after the one team scores a 6 point touchdown. So it is not possible to score 1 point if the other team has less than 6 points. This means the scores that are not possible to get are the following: 0-1 1-1 2-1 3-1 4-1 5-1 7-1 The score 1-1 is the only one where both teams have impossible point totals. Thanks to Matt Johnson for being the first person to point out the rule change and conclude that 7-1 is the highest impossible score.
Janzen Aguilar-Nelson And they likely never will be to score that many points with a touchdown being only 6 points. Stupid to say it is theoretically possible.
David James do you know what the word "theoretical" means? lmao in your response you even said they "LIKELY never will be able to score..." which implies that it is, in fact, theoretically possible.
Could you also argue that ridiculously large scores are also impossible to get due to the fact that there is a time limit for each football game? So it would be physically impossible for A=10^1234321 and B=990^21342202.
It is also possible to score 1 point by a defensive 1-point safety. However, this can only happen if the other team scored a touchdown, which means that 6-1 is possible. However, 7-1 is impossible, as well as 5-1, 4-1, 3-1, 2-1, 1-1, and 1-0.
Yes, there is a 1 point safety on a 2 point conversion if the people who caused the turnover gl back into their own end zone. However, that would require a touchdown, worth 6 points.
Based on the rules in all previous seasons, 40-1, 50-1, 60-1, etc are all impossible, and are bigger than 1-1. But now with some recent rule changes, in theory, it's possible for a team to score a single point with a 1-point safety (in practice, a team having exactly one point will never happen, but it is theoretically possible). With the new rules applied, I think the largest impossible score is 7-1.
+Matt Johnson You are correct. As others are pointing out, there are many impossible scores involving 1 point. I solved for the requirement that both A and B need to be impossible point totals, and I'll add a note for that.
Here's a link about the new rule in the NFL: profootballtalk.nbcsports.com/2015/05/22/nfl-may-see-its-first-one-point-safety/ And Wikipedia explains "A conversion safety could also be scored by the defense in a score in college football [now in the NFL as well]; although this has never occurred, it is the only possible way a team could finish with a single point in an American football game" en.wikipedia.org/wiki/Safety_(gridiron_football_score)
+Matt Johnson Actually it's still theoretically impossible for a team to have exactly one point because a 1-point safety will give the offense one point after they've just scored a touchdown. Essentially it's like converting an extra point. Also, I need to be "that guy" and point out that this video never specified that A and B have to be integers (or even real), so there are an infinite number of solutions larger than 1-1.
+I_Hate_Google_So_Much It's true that the offense can score a one point safety, making it like an extra point. But the defense can, too (it's just never happened and probably never will). Picture this: Let's say a team scores a touchdown, and it's 6-0. They line up for the PAT, and it gets blocked. A defender scoops up the ball and starts running the other way. He's covered 90 yards and it looks like he's about to score 2 points when he gets caught from behind and fumbles. The ball stays in the field of play and does not roll into the end zone. A guy from the kicking team scoops up the fumble, and turns to head back 90+ yards or so. He sees a few defenders, so he first runs backward thinking he can escape them. He runs back into his own end zone and gets tackled there. The defense has scored a safety. The score is now 6-1.
Wouldn't any score be impossible if either team only has one point? So the score 1-21 would also be valid as an "impossible score" unless we are assuming the problem means "both A and B are impossible scores".
0 - 0 is the only score guaranteed to occur in every single game. Since 0 is always available then you would have to include every single occurrence of a 1 - x score or x - 1 score.
To all of you folks asking if a really high score is possible: yes. It is, in fact, possible to score a touchdown without taking any time off the clock. This happens on a kickoff if the team that is supposed to return the ball does not touch it, and the kicking team recovers the ball in the end zone. Most recently, the Jets did this against the Bills in the 2016-17 season.
@@Joe-rz3fd As of 2018, if a ball gets to the end zone and touches the ground, it’s an automatic touchback. There’s no need for a returning-team player to pick it up and kneel, or even catch a ball if it’s headed for the end zone and they don’t intend to return it. The play you reference is fun to watch and, to your point, took no time off the clock. But, as of 2018, that play can no longer happen.
The largest finite impossible score is 7-1, by virtue of the rare 1 point safety play by current NFL rules. If team A scores a TD, goes for two points and the ball is intercepted by team B and returned nearly 100 yards but fumbled before breaking the plane of the other end zone, and team A recovers the ball in the other end zone and tackled, team B would earn the one point safety, making the score 6-1, a possible score. Since team A cannot score 1 point without team B scoring a touchdown, the largest impossible score must be 7-1.
If the ball travels across the goal line on its own impetus after being fumbled in the field of play during the return, and the other team recovers in the endzone, the scoring team does not get the one-point safety. If the ball is recovered in the field of play, and *then* run into the team's own endzone and tackled, the safety comes into play (Rule 11, Section 3, Article 2c).
I don't know much about NFL, but from what i do know, the game is played on a field with length, in a limited amount of time, and with players who have mass that can't move faster than light. So, it takes some time to score any amount of point, which means there is a limit to how many points are possible in a single game, which means that the highest a+b is infinity and not 2.
A kickoff in which the kicking team recovers the ball in the end zone without the recieving team touching it results in the kicking team scoring and no time leaving the clock. No time plays during a pat. You can score without taking any time off the clock.
This is actually incorrect because the clock is not always running and there is one very rare way to score without the clock running that while it is highly unlikely to occurs could be repeated infinetky without breaking the laws of physics or the rules of the game meaning scoring potential is infinite in american football at the NFL level.
Besides the previous mistakes that you already corrected, I would do this: the scoring rules should be explained *before* you ask us to pause and try it ourselves. BTW I think it's easier to think of it as even and odd numbers. Since a safety is 2 points, any even number is possible. For odd numbers, start at 3 and repeatedly add 2. That will give you all the odd numbers except 1. None of these are math errors, just ergonomic suggestions.
Just a footnote. In the NFL, a forfeit results in a 2-0 final score. Under most other American football league rules, in particular NCAA, a forfeit results in a 1-0 final score.
What if we exclude 1 and 2 point safeties. Then what's the highest possible impossible score only using scores of 3 (field goals) and 6,7,8 (touchdowns)?
Actually it's even simpler than you said because any even number 2n can be made by n safeties and any odd number 2n + 1 = 2(n - 1) + 3 can be made with (n - 1) safeties and one field goal.
I think I got a liittle confused by the problem's parameters , especially towards the end. Like isn't 14-1 an impossible score? In the 'Canadian Football League" rules there are ways to earn only a single point.
But why overcomplicate it so much with those triplets? Since 0 is possible and 2 is possible, then every even number is possible. And since every even number is possible and 3 is possible, then every odd number >=3 is also possible. Therefore the only impossible number is 1 and the score is impossible if and only if one of the two numbers equals 1.
Yes, there is a 1-point safety. The NFL made the 1-point safety possible in 2015 (I believe), but the NCAA has had it for many years. However, a 1-point safety can only occur on a conversion attempt, meaning the team attempting the conversion has scored a touchdown (6 points). The offense can score a 1-point safety if the defense, when attempting to return a failed conversion is tackled in the end zone. The defense can score a 1-point safety if the offensive team bungles the conversion so badly that a safety is scored, meaning a loss of up to 98 yards (NFL) or 97 yards (NCAA), This is extremely unlikely, but not impossible. A 6-1 score is possible, but 1-0. 1-1, 2-1, 3-1, 4-1, 5-1, and 7-1 are not. Any other X-1 score is possible.
I think you messed up here Presh. The real answer is 7-1. You can score a touchdown and then try to kick a field goal extra point, but have the other team deflect it and run it back for one point, but if you score that one point, then the opposing team will only score six. Since there is no other way to score one point, the largest impossible NFL score is 7-1.
File this under Presh is human and humble. I have thought about this puzzle (or similar) in the past, for example in Super Bowl pools where you are randomly assigned a single digit representing the last digit in a football score. I ponder what digits are the best to get. I didn't reach any conclusion about that, but one thing I did conclude is that every score is possible (except for 1 of course)
If I'm not mistaken, a 1 point safety occurs when the kick is blocked, recovered by the blocking team, brought from the field of play into their own endzone and then tackled. I believe what you are referencing where an extra point is blocked and returned into the kicking team's endzone results in 2 points for the blocking team. Therefore I would imagine any score to 1 is impossible to achieve
If the kick is blocked, taken almost all the way to the other end of the field, fumbled, recovered by the kicking team, taken back into their own endzone, and then they are tackled there, that's a one point safety for the return team. If that touchdown and safety were the only scoring plays of the game, the final score would be 6-1.
A team can score 1 point on an extra point safety. This qualifies that the opponent must score at least six so that the other team would have the opportunity to score 1 point. Therefore, 0-1, 1-1, 2-1, 3-1, 4-1 and 5-1 are all impossible. There is a scenario where 6-1 exists.
one pair of unlawful scores is 1 and 1, that sums to 2. another pair of unlawful scores are: pi to the power of a billion and pi to the power of two billion. that sums to a number bigger than 2.
Can we say that it is mathematically impossible to score higher than 8 times the number of seconds in a game? That is, no higher than 28,800? I realize there are some untimed plays. Two teams theoretically could trade free kicks to infinity, and accumulate absurdly long field goals without any time coming off the clock. In light of that, I suppose every number is possible.
I got that answer. If you multiply the number of seconds in a game by 1000, there is no way that a team could score that many points. Humans have a maximum running speed, and throwing speed, and kicking speed. Any score above that would also be impossible.
I was thinking along the lines of negative numbers (so both A and B could be any number lower than 0). And later in the form of non-whole numbers. So that A could be equal to pi, or root 7.
How do you score only 1 point in NFL football? If the defense gets the ball in the field of play on a conversion attemp, and then a defensive player takes the ball into his own end zone and is tackled, the result will be a one-point safety: The offensive team will get one point. That has never happened before in NFL history.(22 mag 2015)
Actually, a one point is achievable. If a PAT is blocked and the defence recovers it, they can run it to the endzone and score a point. Similar to field goals.
This would score two points. A one point safety can only be achieved when a two point try is intercepted, returned 99 yards, fumbled, and recovered by the team going for the two point try in the other end zone. By this logic, the largest impossible score is 7-1, since a 6-1 game is possible, but one team cannot score 1 point without a TD from the other team.
A is 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 and B is 0.
+NoriMori He did at the beginning of the video. He showed what points were possible in different scoring situations. He then showed examples of possible scores setting up the demonstration of what scores were impossible... because if it's not a possible score, then it's impossible.
creepy99 If he says that anywhere, it's obviously after the "give this problem a try" part. Obviously I'm not going to watch that part if I haven't tried the problem. And I can't try the problem if I don't already know what an impossible NFL score (or any NFL score) would look like.
A = B = 1; A + B = 2 Starting with 0, the only impossible score a team can have is 1. The only possible way to score 1 point is on a PAT (point after touchdown), and that can be done only after scoring 6 points for a TD. A safety is 2 points. A field goal is 3 points. Every integer greater than those, can be made as a positive integer linear combination of those, and is therefore a possible score. Not having watched the vid yet, I'm wondering how Presh wastes almost 4 minutes on no more than this. OK, he goes into extra detail about the argument above, and more than necessary amount of argument at that; all he has to do is, starting with just the 2 & 3, add any number of 2's to the 2 to get all the even scores, and to the 3 to get all the odd scores. Of course, multiple field goals are *way* more common than multiple safeties, but this riddle isn't about likelihood; it's about what's actually (mathematically) possible. Note: I was taking the statement of the problem to be that both scores, A and B separately, had to be impossible.
No. You can only go so high as American football has a time limit. Try to get one hundred million dolla... Points, 100,000,000 points. Even with both teams working together, I don't see this happening.
Actually according to NFL rules a one point safety is achievable if one team is trying to go for 2 and somehow a safety occurs the impossible scores are 1-0 1-1 1-2 1-3 1-4 and 1-5
1-0. That is the only impossible score in American Football. Every other score is possible; assuming not limited by time. Do a search here on UToob for _"Scoriagami."_
Why did you consider the 4,5,6 triplet of numbers? can't you just consider 4 and 5 and then add two points to each of them by adding 2? note that i am not familiar to NFL rules and i'm just assuming that you can get the 2 points more than once (mostly because you got 4 by adding 2 with 2)
This is totally incorrect. To make an impossible score, only one team’s score needs to be 1. So an impossible score is 1 - N, where N is any integer. Since the problem was to find the highest total score that is impossible, the score of 1 - 10000 is also impossible, and it has a much higher total than 1 - 1. It’s also impossible to score a fractional amount of points, so 10.5 - 17.5 is also an impossible score, which has a higher total than 1 - 1. Imaginary numbers are also impossible. The latter 2 cases may sound like nit picking, but given that this channel also puts forth problems like “A ship transports 100 goats from China to Malaysia, how old is the ship’s captain?” (or some such nonsense), and then proceeds to make all kinds of crazy assumptions about the legalities of boat captain’s ages in various countries in an attempt to argue a sensible solution. So if loose interpretation is good for one problem, it’s good for another problem.
How about the score 11-10? It's pretty close to "impossible" since it's only ever happened in 1 NFL game in their entire history (Nov 16, 2008 - PIT 11, SD 10) ;-) Interesting reading... blogs.wsj.com/numbers/how-unlikely-was-the-historic-11-10-score-458/
Pausing before solution ... I must not be understanding something. All nonnegative integers are possible NFL single-team game scores, except 1. So the only two-team game score in which both sides are impossible scores would be 1-1. That wouldn't be a very interesting answer, and then why even specify that A+B must be maximized, when there is only one option? I suppose I'm missing something. Solution time.
So I wasn't missing anything. I guess the idea was that it may be counterintuitive that any score but 1 is possible in football. Obvious to me, but I suppose only because I'm highly interested in math and football!
A 1-point safety can be scored by either offense or defense on a conversion attempt. The defensive safety is what would give a final score of x-1. But yes, 2-1 is impossible, as are 1-0, 1-1, 3-1, 4-1, 5-1, and 7-1.
How are two numbers relatively primes? They are either primes or they are not. Also that question is unfair. Most of the world probably don't even know what NFL is or what the rules of american football are.
+FalcoGer Relative primes means that there is NO natural number bigger than 1 that divides both numbers individually. Stated another way: list all the prime factors of a and b. If there is no number appearing in both lists, then they are relatively prime. For example: (10, 9), (25, 16), (1000, 1001).
+FalcoGer - You are correct that numbers are indeed prime or not. However, we can use similar terminology for similar properties of numbers. "Relatively prime" doesn't mean "quite prime" or "fairly prime". It means "these two (or more) numbers are prime, relative to each other". Another term is "co-prime". It means that they do not share a factor, other than 1. Prime numbers have no factors, other than themselves and 1. "Relatively prime" or "co prime" numbers have no factors in common. Being coprime with another number is a less severe restriction than being prime. Indeed, one way to imagine it is that prime numbers are numbers that are coprime with every other number!
See, there are some flaws in this problem. One has been pointed out multiple times, where 1 is impossible, but 0 _is_ possible; therefore by including 1-0 or 0-1, you must also include any X-1, thus making the total potentially infinite. Even though you've fixed for that, there are still some issues. The question asked for _impossible_ scores, but never required the scores to be integers. So 7.5-4.5 are also valid answers, since football does not award half-points. There is also no rule saying the scores cannot be negative. Sure, there is no way to obtain a negative score in football, but that's basically the whole point of the problem, as a score of 1 is also impossible to obtain. Not only can the answers be infinite, but it can also be _negatively infinite_. Furthermore, while football is scored in using numeric values, this is not true for everything. For example, school grades are a type of scoring system that uses letters of the alphabet. Football can never have a score of B-F, thus making this another impossible score. To make things worse, there's no reason to allow for completely absurd scores, as games can be made to account for them. This is particularly true for joke rating systems, as people might be asked to rate a product/event on a scale of 1 to _x_ where _x_ can literally be substituted by anything, such as "nuclear fission". Since this scoring system is not utilized by the NFL, a score of coffee-alligator is not possible, thus a valid answer. In conclusion, impossible scores are not just infinite or negatively infinite; they are *_multi-dimensionally infinite_*!
103-1 is possible. Team A scores 14 touchdowns and converts extra points 13 times. That's 97 points. Then, Team A scores a 15th touchdown, but a serious of unfortunate events causes a defensive safety on the conversion, which is a 1-point safety, leaving the final score 103-1.
I noticed that you said the last tie occurred in 1943. There have been over 100 ties since then, with the last being in 2014 between Carolina and Cincinnati.
Any score with either team having 1 is impossible! A PAT comes after a TD, a 1 point safety comes after a TD with the same team who scored the TD scoring the safety (essentially making up for a blocked PAT). A safety in which the other team scores is 2 points, not 1 so no team can have 1 as their score!
You're thinking too narrow. The PAT happens near one end zone, and you're thinking about results that occur when the ball ends up in that end zone. The 1 point safety for the other team would have to be some very unlikely scenario that gets the ball to the *other* end zone.
I don't get what the point of all the math was, extremely unnecessary, every who knows anything about football knows 1 is the only impossible score, and even if u didn't the math didn't make it easier or shed anything insightful, it was all super basic
There are an infinite number of impossible scores as long as one team scores 1 point. The other team could score 1000 points but the score is still impossible due to the invalid score of one by the other team
This "solution" is absolute crap! It is impossible to score 1 million points in a regulation football game because it is a timed game so there is no solution to this question. Time will eventually run out. There is no largest impossible score. Stupid question. Thumbs down!
+David James not true. in theory, humans could evolve to be faster than the speed of light and easily reach over a million points. The scores in this video cannot be reached even in theory
Janzen Aguilar-Nelson Very stupid answer on your part. The question is asking an impossible NFL score now, not in the future. If future was allowed then the answer is unknown cuz they could just change the rules of football.
David James very stupid reply on your part. Nowhere in the question does it say "impossible score now and not in the future." Also, changing the rules of football fundamentally changes the problem, while merely changing the speed at which we believe it to be "possible" to score does not fundamentally change the problem. You clearly have very little to no experience in dealing with theoreticals
Very sorry, you guys are correct and my video is wrong. I only present the answer if both A and B are impossible scores to attain. I have put a note in the video.
+Reticality Yes 1-1 is the only doubly impossible score. It is also impossible for NFL games to end as 1-0 or 0-1.
+MindYourDecisions True, but that goes for any X - 1 or 1 - X.
+MindYourDecisions Actually, if one team forfeits, the game goes into the books as a 1-0 victory. 1-1 is impossible, though.
+Gregory Pietsch Not true in the NFL. Forfeit is 2-0.
Unfortunately this whole problem does not work, as there is a rare way to score a single point in American football (occurred only twice in the NCAA and not once since 1940 in NFL) thus you can literally have all positive whole numbers and 0 as scores
You've explained why each number can be attained in a very cumbersome way, once you have 2 and 3 it's obvious that you can reach every even number (just keep adding 2's) and every odd number besides 1 (just start with 3 and keep adding 2's). Therefore you can reach all numbers.
Only in America would they rename a mathematical problem "The chicken McNugget problem".
It's to find the smallest number of chicken mcnuggets impossible to get if you use all of the nuggets in each pack
What scores are not possible to get to in an NFL game? That is what I originally wanted to answer but I messed up in the video.
A recent NFL rule change also allows for 1 point safeties. If one team scores a touchdown (6 points) and goes for a 1 point conversion but messes up the point-after kick, the team on defense can return that for 1 point--called a 1 point safety. (In the past the play was ruled dead if the defense blocked the kick).
So this means a score of 6-1 is possible.
Then, since it's possible to get to 6-1, it is also possible to get to 8-1, 9-1, and so on since a team can then increase its score by any number larger than 2 (as shown in the video).
The 1 point safety only occurs after the one team scores a 6 point touchdown. So it is not possible to score 1 point if the other team has less than 6 points.
This means the scores that are not possible to get are the following:
0-1
1-1
2-1
3-1
4-1
5-1
7-1
The score 1-1 is the only one where both teams have impossible point totals.
Thanks to Matt Johnson for being the first person to point out the rule change and conclude that 7-1 is the highest impossible score.
+MindYourDecisions Highest impossible score (my ass). What about 1 million to 500,000? Is that possible?
Ur an idiot haha the return is worth 2 points
+David James still theoretically possible. Humans just aren't fast enough yet
Janzen Aguilar-Nelson And they likely never will be to score that many points with a touchdown being only 6 points. Stupid to say it is theoretically possible.
David James do you know what the word "theoretical" means? lmao in your response you even said they "LIKELY never will be able to score..." which implies that it is, in fact, theoretically possible.
Could you also argue that ridiculously large scores are also impossible to get due to the fact that there is a time limit for each football game? So it would be physically impossible for A=10^1234321 and B=990^21342202.
I think it is not true. Because 1-87, 1-55, 16-1, 47-1 was stil impossible score!
+YaKuN You are correct, thanks. I solved for if both teams had impossible point totals. I am adding a note to that effect.
please explain
Unfortunately, the updated rulebooks have now made one-points incredibly unlucky but possible. All those scores mentioned are possible.
The correct answer to the way it is worded and the rules is 7-1 is the highest impossible score.
5-1 because you can the other team has to get a touchdown for you to get a 1 p.o. conversion
No the only impossible scores are 1-0, 1-1, 1-2, 1-3, 1-4, 1-5, and 1-7. Due to the extremely rare one point safety.
This is the answer.
It is also possible to score 1 point by a defensive 1-point safety. However, this can only happen if the other team scored a touchdown, which means that 6-1 is possible. However, 7-1 is impossible, as well as 5-1, 4-1, 3-1, 2-1, 1-1, and 1-0.
Finally, FOOTBALL. I got it right. Glad you threw me a bone.
Um, A>1,000,000 or more and -1
shouldn't 1 - 0 and 0 - 1 also be disqualified because 0 is possible? or am i missing something here?
Yeah zero is possible. He messed up.
Well, technically, if one team forfeits, the final score goes into the books as 1-0. So the ONLY truly impossible score is 1-1.
Darrel Jones No, if an opposing team forfeits, then the other team, if ready and willing to play, wins with a result of 2-0.
Technically, 0 is not an impossible score. If the team that had 0 did nothing, they would have 0.
Yes, there is a 1 point safety on a 2 point conversion if the people who caused the turnover gl back into their own end zone. However, that would require a touchdown, worth 6 points.
Sorry, as many say below, 7-1, is the largest impossible score, see jon Bois video on scoragami. Any replies coming my way?
The score 6-1 is possible but 7-1 is not
7-1 is also an impossible score, and it's larger that 1-1
Based on the rules in all previous seasons, 40-1, 50-1, 60-1, etc are all impossible, and are bigger than 1-1. But now with some recent rule changes, in theory, it's possible for a team to score a single point with a 1-point safety (in practice, a team having exactly one point will never happen, but it is theoretically possible). With the new rules applied, I think the largest impossible score is 7-1.
+Matt Johnson You are correct. As others are pointing out, there are many impossible scores involving 1 point. I solved for the requirement that both A and B need to be impossible point totals, and I'll add a note for that.
Here's a link about the new rule in the NFL:
profootballtalk.nbcsports.com/2015/05/22/nfl-may-see-its-first-one-point-safety/
And Wikipedia explains "A conversion safety could also be scored by the defense in a score in college football [now in the NFL as well]; although this has never occurred, it is the only possible way a team could finish with a single point in an American football game"
en.wikipedia.org/wiki/Safety_(gridiron_football_score)
+Matt Johnson Thanks for the links!
+Matt Johnson Actually it's still theoretically impossible for a team to have exactly one point because a 1-point safety will give the offense one point after they've just scored a touchdown. Essentially it's like converting an extra point.
Also, I need to be "that guy" and point out that this video never specified that A and B have to be integers (or even real), so there are an infinite number of solutions larger than 1-1.
+I_Hate_Google_So_Much It's true that the offense can score a one point safety, making it like an extra point. But the defense can, too (it's just never happened and probably never will). Picture this: Let's say a team scores a touchdown, and it's 6-0. They line up for the PAT, and it gets blocked. A defender scoops up the ball and starts running the other way. He's covered 90 yards and it looks like he's about to score 2 points when he gets caught from behind and fumbles. The ball stays in the field of play and does not roll into the end zone. A guy from the kicking team scoops up the fumble, and turns to head back 90+ yards or so. He sees a few defenders, so he first runs backward thinking he can escape them. He runs back into his own end zone and gets tackled there. The defense has scored a safety. The score is now 6-1.
A 1 point safety does exist on two point conversions. Look up Jon Bois’ scorigami video for info on it
Wouldn't any score be impossible if either team only has one point? So the score 1-21 would also be valid as an "impossible score" unless we are assuming the problem means "both A and B are impossible scores".
+Sweaves You are correct, thanks. I will add the requirement that "both A and B should be impossible scores."
0 - 0 is the only score guaranteed to occur in every single game. Since 0 is always available then you would have to include every single occurrence of a 1 - x score or x - 1 score.
To all of you folks asking if a really high score is possible: yes. It is, in fact, possible to score a touchdown without taking any time off the clock. This happens on a kickoff if the team that is supposed to return the ball does not touch it, and the kicking team recovers the ball in the end zone. Most recently, the Jets did this against the Bills in the 2016-17 season.
Can no longer do this as of 2018 ... so, I think even when this post was originally made, it was no longer true.
@@67L48 What are you talking about?
@@Joe-rz3fd As of 2018, if a ball gets to the end zone and touches the ground, it’s an automatic touchback. There’s no need for a returning-team player to pick it up and kneel, or even catch a ball if it’s headed for the end zone and they don’t intend to return it.
The play you reference is fun to watch and, to your point, took no time off the clock. But, as of 2018, that play can no longer happen.
The largest finite impossible score is 7-1, by virtue of the rare 1 point safety play by current NFL rules. If team A scores a TD, goes for two points and the ball is intercepted by team B and returned nearly 100 yards but fumbled before breaking the plane of the other end zone, and team A recovers the ball in the other end zone and tackled, team B would earn the one point safety, making the score 6-1, a possible score. Since team A cannot score 1 point without team B scoring a touchdown, the largest impossible score must be 7-1.
If the ball travels across the goal line on its own impetus after being fumbled in the field of play during the return, and the other team recovers in the endzone, the scoring team does not get the one-point safety. If the ball is recovered in the field of play, and *then* run into the team's own endzone and tackled, the safety comes into play (Rule 11, Section 3, Article 2c).
I don't know much about NFL, but from what i do know, the game is played on a field with length, in a limited amount of time, and with players who have mass that can't move faster than light.
So, it takes some time to score any amount of point, which means there is a limit to how many points are possible in a single game, which means that the highest a+b is infinity and not 2.
This is not only correct, but super obvious. Glad someone pointed it out. What a stupid video!
This is not only correct, but super obvious. Glad someone pointed it out. What a stupid video!
The video isn't stupid, it is meant to be a trick question but physics tricked its trick.
That was a weird sentence.
A kickoff in which the kicking team recovers the ball in the end zone without the recieving team touching it results in the kicking team scoring and no time leaving the clock. No time plays during a pat. You can score without taking any time off the clock.
This is actually incorrect because the clock is not always running and there is one very rare way to score without the clock running that while it is highly unlikely to occurs could be repeated infinetky without breaking the laws of physics or the rules of the game meaning scoring potential is infinite in american football at the NFL level.
I am suppose to solve the problem at 0:27, but the critical information is first given at 0:30.
Besides the previous mistakes that you already corrected, I would do this: the scoring rules should be explained *before* you ask us to pause and try it ourselves.
BTW I think it's easier to think of it as even and odd numbers. Since a safety is 2 points, any even number is possible. For odd numbers, start at 3 and repeatedly add 2. That will give you all the odd numbers except 1.
None of these are math errors, just ergonomic suggestions.
I don't know anything about American football…
This is the one problem in your series that you do not need any math to solve.
Just a footnote. In the NFL, a forfeit results in a 2-0 final score. Under most other American football league rules, in particular NCAA, a forfeit results in a 1-0 final score.
Sorry for being the smart***, but non-whole number scores are also impossible, so the largest impossible score is infinite.
What if the game went on for an infinite amount of time?
+Zyph_Legend You forgot the comma!
...9999999999.1 is also impossible.
+Koray Acar where would I need a comma in my comment?
+Zyph_Legend what if, the game went on for an infinite amount of time
the comma can be used or not
+yusef shehata, the comma in your comment is completely redundant as it serves not grammatical purpose.
Why is 1-1 is the largest impossible score? Any number, up to infinity - to 1 is also impossible, and it does not have upper limit at all.
What if we exclude 1 and 2 point safeties. Then what's the highest possible impossible score only using scores of 3 (field goals) and 6,7,8 (touchdowns)?
That would be 5.
And if we simplify further and limit ourselves to field goals and 7-point touchdowns, it's 11.
Actually it's even simpler than you said because any even number 2n can be made by n safeties and any odd number 2n + 1 = 2(n - 1) + 3 can be made with (n - 1) safeties and one field goal.
Any score that has a one on either side is impossible, so theoretically talking it could to one team having infinite points and the other having.
1-27384826273 is also an imposseble score
I think I got a liittle confused by the problem's parameters , especially towards the end. Like isn't 14-1 an impossible score?
In the 'Canadian Football League" rules there are ways to earn only a single point.
But why overcomplicate it so much with those triplets? Since 0 is possible and 2 is possible, then every even number is possible. And since every even number is possible and 3 is possible, then every odd number >=3 is also possible. Therefore the only impossible number is 1 and the score is impossible if and only if one of the two numbers equals 1.
Isn't there a 1 point safety?
Yes, there is a 1-point safety. The NFL made the 1-point safety possible in 2015 (I believe), but the NCAA has had it for many years. However, a 1-point safety can only occur on a conversion attempt, meaning the team attempting the conversion has scored a touchdown (6 points). The offense can score a 1-point safety if the defense, when attempting to return a failed conversion is tackled in the end zone. The defense can score a 1-point safety if the offensive team bungles the conversion so badly that a safety is scored, meaning a loss of up to 98 yards (NFL) or 97 yards (NCAA), This is extremely unlikely, but not impossible.
A 6-1 score is possible, but 1-0. 1-1, 2-1, 3-1, 4-1, 5-1, and 7-1 are not. Any other X-1 score is possible.
I think you messed up here Presh. The real answer is 7-1.
You can score a touchdown and then try to kick a field goal extra point, but have the other team deflect it and run it back for one point, but if you score that one point, then the opposing team will only score six. Since there is no other way to score one point, the largest impossible NFL score is 7-1.
File this under Presh is human and humble.
I have thought about this puzzle (or similar) in the past, for example in Super Bowl pools where you are randomly assigned a single digit representing the last digit in a football score. I ponder what digits are the best to get. I didn't reach any conclusion about that, but one thing I did conclude is that every score is possible (except for 1 of course)
If I'm not mistaken, a 1 point safety occurs when the kick is blocked, recovered by the blocking team, brought from the field of play into their own endzone and then tackled. I believe what you are referencing where an extra point is blocked and returned into the kicking team's endzone results in 2 points for the blocking team. Therefore I would imagine any score to 1 is impossible to achieve
If the kick is blocked, taken almost all the way to the other end of the field, fumbled, recovered by the kicking team, taken back into their own endzone, and then they are tackled there, that's a one point safety for the return team.
If that touchdown and safety were the only scoring plays of the game, the final score would be 6-1.
A team can score 1 point on an extra point safety. This qualifies that the opponent must score at least six so that the other team would have the opportunity to score 1 point.
Therefore, 0-1, 1-1, 2-1, 3-1, 4-1 and 5-1 are all impossible. There is a scenario where 6-1 exists.
Also meaning that 7-1 is impossible.
Assuming what we know is correct, the highest possible score is by moving just under the speed of light and score touchdowns so...?
Neither do non-intergal scores.
one pair of unlawful scores is 1 and 1, that sums to 2. another pair of unlawful scores are: pi to the power of a billion and pi to the power of two billion. that sums to a number bigger than 2.
0-0 is NOT an impossible score. 7 November 1943 between the Detroit Lions and New York Giants.
YaKuN is also correct!
Can we say that it is mathematically impossible to score higher than 8 times the number of seconds in a game? That is, no higher than 28,800?
I realize there are some untimed plays. Two teams theoretically could trade free kicks to infinity, and accumulate absurdly long field goals without any time coming off the clock. In light of that, I suppose every number is possible.
Only one of the variables has to be 1 for the whole score to be impossible, so A could be 1 and B could be infinite
I got that answer. If you multiply the number of seconds in a game by 1000, there is no way that a team could score that many points. Humans have a maximum running speed, and throwing speed, and kicking speed. Any score above that would also be impossible.
I thought u said that both a and b have to be impossible. It is very possible for a team to not score any points so the ONLY impossible score is 1-1
I was thinking along the lines of negative numbers (so both A and B could be any number lower than 0). And later in the form of non-whole numbers. So that A could be equal to pi, or root 7.
l'd love to see a pi-point play...
It is possible to get a 1 point safety nowadays.
How do you score only 1 point in NFL football?
If the defense gets the ball in the field of play on a conversion attemp, and then a defensive player takes the ball into his own end zone and is tackled, the result will be a one-point safety: The offensive team will get one point. That has never happened before in NFL history.(22 mag 2015)
Actually, a one point is achievable. If a PAT is blocked and the defence recovers it, they can run it to the endzone and score a point. Similar to field goals.
This would score two points. A one point safety can only be achieved when a two point try is intercepted, returned 99 yards, fumbled, and recovered by the team going for the two point try in the other end zone. By this logic, the largest impossible score is 7-1, since a 6-1 game is possible, but one team cannot score 1 point without a TD from the other team.
0-0 in the playoffs is impossible 😏
big fax
A is 999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 and B is 0.
And, if the game is of a random mathematically existing number, it could only be and can be any type of 1. (i.e. -1, 1, i, -i, i+1,...)
Would've been nice if you'd explained what constitutes an impossible NFL score for those of us who are sports-illiterate.
+NoriMori He did at the beginning of the video. He showed what points were possible in different scoring situations. He then showed examples of possible scores setting up the demonstration of what scores were impossible... because if it's not a possible score, then it's impossible.
creepy99 If he says that anywhere, it's obviously after the "give this problem a try" part. Obviously I'm not going to watch that part if I haven't tried the problem. And I can't try the problem if I don't already know what an impossible NFL score (or any NFL score) would look like.
A = B = 1; A + B = 2
Starting with 0, the only impossible score a team can have is 1.
The only possible way to score 1 point is on a PAT (point after touchdown), and that can be done only after scoring 6 points for a TD.
A safety is 2 points.
A field goal is 3 points.
Every integer greater than those, can be made as a positive integer linear combination of those, and is therefore a possible score.
Not having watched the vid yet, I'm wondering how Presh wastes almost 4 minutes on no more than this.
OK, he goes into extra detail about the argument above, and more than necessary amount of argument at that; all he has to do is, starting with just the 2 & 3, add any number of 2's to the 2 to get all the even scores, and to the 3 to get all the odd scores.
Of course, multiple field goals are *way* more common than multiple safeties, but this riddle isn't about likelihood; it's about what's actually (mathematically) possible.
Note: I was taking the statement of the problem to be that both scores, A and B separately, had to be impossible.
No. You can only go so high as American football has a time limit. Try to get one hundred million dolla... Points, 100,000,000 points. Even with both teams working together, I don't see this happening.
Actually according to NFL rules a one point safety is achievable if one team is trying to go for 2 and somehow a safety occurs the impossible scores are 1-0 1-1 1-2 1-3 1-4 and 1-5
1-7 is impossible as well.
I would say 10^10000000 - 10^100000000 is an impossible score.
why is 0 points impossible?
Jon Bois has entered the chat
1-0. That is the only impossible score in American Football. Every other score is possible; assuming not limited by time. Do a search here on UToob for _"Scoriagami."_
Weird. 1-anything and anything-1 are all impossible.
Why did you consider the 4,5,6 triplet of numbers? can't you just consider 4 and 5 and then add two points to each of them by adding 2? note that i am not familiar to NFL rules and i'm just assuming that you can get the 2 points more than once (mostly because you got 4 by adding 2 with 2)
This problem must be from Canada or Russia
This is totally incorrect. To make an impossible score, only one team’s score needs to be 1. So an impossible score is 1 - N, where N is any integer. Since the problem was to find the highest total score that is impossible, the score of 1 - 10000 is also impossible, and it has a much higher total than 1 - 1. It’s also impossible to score a fractional amount of points, so 10.5 - 17.5 is also an impossible score, which has a higher total than 1 - 1. Imaginary numbers are also impossible.
The latter 2 cases may sound like nit picking, but given that this channel also puts forth problems like “A ship transports 100 goats from China to Malaysia, how old is the ship’s captain?” (or some such nonsense), and then proceeds to make all kinds of crazy assumptions about the legalities of boat captain’s ages in various countries in an attempt to argue a sensible solution. So if loose interpretation is good for one problem, it’s good for another problem.
Zero is a possible score.
How about the score 11-10? It's pretty close to "impossible" since it's only ever happened in 1 NFL game in their entire history (Nov 16, 2008 - PIT 11, SD 10) ;-)
Interesting reading... blogs.wsj.com/numbers/how-unlikely-was-the-historic-11-10-score-458/
Something that has actually happened is, by definition, not impossible.
Pausing before solution ... I must not be understanding something. All nonnegative integers are possible NFL single-team game scores, except 1. So the only two-team game score in which both sides are impossible scores would be 1-1. That wouldn't be a very interesting answer, and then why even specify that A+B must be maximized, when there is only one option? I suppose I'm missing something. Solution time.
So I wasn't missing anything. I guess the idea was that it may be counterintuitive that any score but 1 is possible in football. Obvious to me, but I suppose only because I'm highly interested in math and football!
Actually a drop kick is worth 1 point... or a 1 point safety... all scores are possible..
Eli Weiss a drop kick is worth 3, and a one point safety requires a touchdown to be scored first.
Wrong, 2-1 is still an impossible score. 19-1, 23-1, any number-1 is impossible
A 1-point safety can be scored by either offense or defense on a conversion attempt. The defensive safety is what would give a final score of x-1. But yes, 2-1 is impossible, as are 1-0, 1-1, 3-1, 4-1, 5-1, and 7-1.
How are two numbers relatively primes? They are either primes or they are not.
Also that question is unfair. Most of the world probably don't even know what NFL is or what the rules of american football are.
+FalcoGer Relative primes means that there is NO natural number bigger than 1 that divides both numbers individually.
Stated another way: list all the prime factors of a and b. If there is no number appearing in both lists, then they are relatively prime.
For example: (10, 9), (25, 16), (1000, 1001).
+FalcoGer - You are correct that numbers are indeed prime or not. However, we can use similar terminology for similar properties of numbers.
"Relatively prime" doesn't mean "quite prime" or "fairly prime". It means "these two (or more) numbers are prime, relative to each other". Another term is "co-prime".
It means that they do not share a factor, other than 1.
Prime numbers have no factors, other than themselves and 1. "Relatively prime" or "co prime" numbers have no factors in common.
Being coprime with another number is a less severe restriction than being prime.
Indeed, one way to imagine it is that prime numbers are numbers that are coprime with every other number!
Moleo Yeah, I learnt this as "co-prime" at school. I'd never heard the term "relatively prime" before seeing this video
See, there are some flaws in this problem. One has been pointed out multiple times, where 1 is impossible, but 0 _is_ possible; therefore by including 1-0 or 0-1, you must also include any X-1, thus making the total potentially infinite. Even though you've fixed for that, there are still some issues. The question asked for _impossible_ scores, but never required the scores to be integers. So 7.5-4.5 are also valid answers, since football does not award half-points. There is also no rule saying the scores cannot be negative. Sure, there is no way to obtain a negative score in football, but that's basically the whole point of the problem, as a score of 1 is also impossible to obtain. Not only can the answers be infinite, but it can also be _negatively infinite_. Furthermore, while football is scored in using numeric values, this is not true for everything. For example, school grades are a type of scoring system that uses letters of the alphabet. Football can never have a score of B-F, thus making this another impossible score. To make things worse, there's no reason to allow for completely absurd scores, as games can be made to account for them. This is particularly true for joke rating systems, as people might be asked to rate a product/event on a scale of 1 to _x_ where _x_ can literally be substituted by anything, such as "nuclear fission". Since this scoring system is not utilized by the NFL, a score of coffee-alligator is not possible, thus a valid answer. In conclusion, impossible scores are not just infinite or negatively infinite; they are *_multi-dimensionally infinite_*!
wrong solution, 17-1 is also impossible.
Jon Bois anyone?
103-1 is a impossible score! 95-1 isnt.
103-1 is possible. Team A scores 14 touchdowns and converts extra points 13 times. That's 97 points. Then, Team A scores a 15th touchdown, but a serious of unfortunate events causes a defensive safety on the conversion, which is a 1-point safety, leaving the final score 103-1.
I noticed that you said the last tie occurred in 1943. There have been over 100 ties since then, with the last being in 2014 between Carolina and Cincinnati.
He said last tie ending 0-0. Listen more carefully.
Infinity is impossible
One is impossible.
Answer: INFINITY + ONE !!!
Well, I suppose if you allow for ties,
Answer: INFINITY * 2
1-1 is impossible.
Also 2-1, 3-1,
Any score with either team having 1 is impossible! A PAT comes after a TD, a 1 point safety comes after a TD with the same team who scored the TD scoring the safety (essentially making up for a blocked PAT). A safety in which the other team scores is 2 points, not 1 so no team can have 1 as their score!
You're thinking too narrow. The PAT happens near one end zone, and you're thinking about results that occur when the ball ends up in that end zone. The 1 point safety for the other team would have to be some very unlikely scenario that gets the ball to the *other* end zone.
Both are -1. Problem solved. Get Rekt
Uh sorry. My bad. I missed the "maximize"
I don't get what the point of all the math was, extremely unnecessary, every who knows anything about football knows 1 is the only impossible score, and even if u didn't the math didn't make it easier or shed anything insightful, it was all super basic
So if 0-1 and 1-0 are impossible, then any value to 1 would be impossible since 0 is a possible score.
A = B = ∞
Here's one, negative ex and negative y
1-1, duh
infinity-1
this video is just rife with mistakes -- I would pull it from the rotation.
7-1
is impossible
1-1
There are an infinite number of impossible scores as long as one team scores 1 point. The other team could score 1000 points but the score is still impossible due to the invalid score of one by the other team
2-1, 3-1, 4-1, 5-1, and 7-1 are impossible.
6-1, 8-1 and any higher total against 1 are all possible.
2.
Infinite to infinite
2x infinite
😡😡😡
Oh I'm sorry, that was just my inner mathematician saying infinity is not a number😡
The
1
just take this video down
-1 - -1
:p
This "solution" is absolute crap! It is impossible to score 1 million points in a regulation football game because it is a timed game so there is no solution to this question. Time will eventually run out. There is no largest impossible score. Stupid question. Thumbs down!
+David James not true. in theory, humans could evolve to be faster than the speed of light and easily reach over a million points. The scores in this video cannot be reached even in theory
Janzen Aguilar-Nelson Very stupid answer on your part. The question is asking an impossible NFL score now, not in the future. If future was allowed then the answer is unknown cuz they could just change the rules of football.
David James very stupid reply on your part. Nowhere in the question does it say "impossible score now and not in the future." Also, changing the rules of football fundamentally changes the problem, while merely changing the speed at which we believe it to be "possible" to score does not fundamentally change the problem. You clearly have very little to no experience in dealing with theoreticals