When the second guy did it, he said any number between 1 and 10M, but it wouldn’t work with single digit numbers, so maybe he should have said between 10 and 10M
My bad, I thought the number you have to subtract was to add, ie 10 would become 11 would make 2, but in fact, it is 10 would become 9. still only works with at least a 2 digit number.
That’s true. If you forget, you could always check with your participant when you first tell them to add the digits. “You do have more than one digit, right?”
It also didn't work with the number I picked. I picked pi, which is a number between 1 and 10 million. But you can't do step 2 to pi, because there are an infinite number of digits in pi. He should have said, pick any *whole* number between 1 and 10 MIllion.
I had this one as soon as Jim presented it. The rule of Nine's. Check your multiplication tables ya'll. Every multiple of nine added together equals 9. And it just keeps going. What gets me is the root. THREE. There is some form of order. Structure following order, or else no universe. Then consider the hexagon. 3 by 3. Quantum physics at work
Here's another version of the trick which also results in the number 9: Take any integer. Reverse its digits. Then subtract the small number from the large number (mathematically-speaking, take the absolute value of the difference of the two numbers). Then start subtracting the sum of the digits of the answer from that answer, and repeat the process as in the original version of the trick. You'll also always get 9 as the final answer. For example, take 3574. Subtract that number from its reverse, 4753. This yields 1179, which is a multiple of 9. Ain't math fun!?
I have had the same half-a-5-cent coin sitting in my wallet ever since you published the original version of the 4.5 coin prediction trick years ago. Well, originally I had both of the halves but I lost one of them at some point. Made with bolt cutters and a file to fix sharp edges.
Yeah I think thats the point of this trick, no one really likes them, surprisingly the guy in the video seems plenty excited about it but I think the main goal is to have someone unimpressively subtracting the numbers only to be impressed and surprised when the half penny trick comes out.
@@BaldMancTwat In a way, the half penny makes it even less Impressive though since it's the final proof that it's just one of these "end up with the same number every time"-thingies.
@@kev3d yeah I can tell how awesome he is just by the fact that he commented on this thread! I love all the videos he does and he deserves more subscribers!
A quick lesson in old (pre 1971) british coins. Before decimalisation, a shilling was worth 12 pence. (and 20 shillings made an old pound). So, four pence and a shilling would have been incorrect. However, before 1970 they minted a 'halfpenny', (Also post-decimalisation, they minted a half-penny from 1972-1984.) so if you wanted to go to a coin shop you could probably get 4 pence and a 'haypinny' and do the trick that way.
I was thinking about this the other day, weirdly. Couldn't remember the exact way you'd generated the number, but came up with something pretty similar. Thanks! :)
I’ve head of a this (with a smaller ranges of numbers) I just refer to it as the trick that always ends in 9. When he said he had half of that amount I knew that’s definitely what it was because that’s a good way to make it look like you weren’t expecting a 9
I knew it. I thought to myself it would be crazy if it came out to a .5 number and he had a half of a penny in there to represent that .5 and he did. That was really cool.
The half-penny is what sells this trick for me. Most of the time once a magician starts giving instructions to do math, it makes me tune out immediately because it screams "mathematicians have constructed this formula to produce the predicted answer," and that's a guaranteed yawn. But this makes it look like a fail state--which normally only happens because the _sucker_ screws up the math--then suddenly redeems it. (Offhand, has anyone you've tried this on ever _assumed_ that they screwed up the math because their number resulted in a seemingly flawed answer before the reveal came out?)
saylor_twift I also thought about this. It might be beneficial if you ask them to get out the calculator app on their phone to simplify any calculations they might do.
@saylor_twift, I would make the instructions very explicit: "Pick any positive whole number between 1000 and 1 Million, like 54367 and write it down. Now, sum the digits of that number and write it below your first number. Now, subtract the two numbers. Now add the digits of that answer and write it under the previous number." Etc. Of course, they could still do the addition and subtraction wrong, but you could have them use a calculator for the calculations :--)
It is a great law in math, the only problem I had is that takes a very long time to write out 164(10[100])1 or 164 and 1 googolplex if in longhand as the trick wants.
definitely want to keep focus on the fact that DJT said between 10 and 10,000,000. Because any number smaller, breaks the trick. He could have messed with Andrew pretty bad, if he wanted to. lol
It'd have been pretty awkward if he had made a mistake during those paper-calculations and came up with 6 or something. What do you magicians do in such case?
I got -9. Does the money fall up from the bag? I didn’t use an integer and treated every digit of the negative as a negative. Even if you only treat the first digit as a negative it doesn’t equal 9.
The only problem with this is that you have to either A: specify 10 or above which gets people suspicious or B: Hope like hell you don't run into the asshole who chooses 4.
If for some reason the person only has 1 number, you could always get them to artificially inflate the number, somehow, like "Multiply that number by 10" - I find these number/math based tricks aren't nearly as impressive because as soon as I start writing down numbers I immediately think "This is going to be a math trick" and my fascination switches gears.
"This week, you prove you're smarter than everyone else, using the powwwerrrr of UNFAIR RIDDLES!!! Mwa ha ha haaaaa!!!" Scam School, yah yah. Scam School, yah yah. "Welcome to the show that's exactly like The Riddler! Only it dresses better. I mean, not by a lot, but... slightly... I mean, it's not wearing a one-piece unitard with a question m... ... Hey, man, welcome to Scam School! The only show dedicated to social engineering at the bar, and on the streets! Hello, beautiful people, I'm Brian Brushwood, and this week we have THREE UNBELIEVABLE RIDDLES! Stuff you can do any time, anywhere, to FrY ThEiR MiNdSsS!!!" -Brian Brushwood, 2015
He said "big" number the first time and said "It can be between 10 and 10,000,000,000 if you like" the second time though... (Also I just checked and it works with 10)
This is really cool and I actually would like to do it.... but my currency doesn't have 1 cent coins, lowest denomination is 5 cents, I'm trying to think something that would have the same impact
I'll bet you one divided by the number of cents I have in my pockets will be one half of the number at the end of this trick. Ready? Pick any finite number, as small or large as you like. Do you have it? Ok... now... Subtract your original number from this number.
Dude blew it right out of the gate...the number needs to be greater than 10...he said pick a number between 1 and whatever.....if he had picked a single digit trick won't work...i pick 6...ok...6-6=0
@@tank2543 My original was 8375.4 11 + 12 + 4 = 27 8375.4 - 27 = 8348.4 11 + 12 + 4 = 27 2 + 7 = 9 Also 12.5 - 8 = 4.5 not 3.5, which equals 9. Sorry mate it works for all numbers in Base 10.
He screwed up by saying 1 to 10 million. You could have written a single digit which would have left a total of zero that's why the first time was between 10 and 10 million.
Here’s exactly how it works for anyone who’s interested. Algebraically, a number can be represented as, N = 10^n(a_n)+10^(n-1)(a_(n-1))+10^(n-2)(a_(n-2))+...+10^1(a_1)+10^0(a_0) Then let’s have, K = a_n + a_(n-1) + a_(n-2) + ... + a_1 + a_0 If we do N - K, we get (10^(n-1))(a_n)+ (10^(n-1)-1)(a_(n-1)) + (10^1 - 1)(a_1) All the tens will become a string of nines where the number of nines is equal to the exponent of the ten. For example, the first is 10n-1 is equal to n amount of nines. If n were 6, that would be 1,000,000 - 1 = 999,999. This means that we can factor out a nine, which means the result of N - K is always a multiple of nine. So the question is, why is it that every multiple of nine will always add up to nine after taking the cross sum until you’ve reached a single digit number is an extension of this. We have, N = 10^n(a_n) + 10^(n-1)(a_(n-1)) + 10^(n-2)(a_(n-2)) + … + 10^1(a_1) + 10^0(a_0) which in this case we’re assuming that N is a multiple of nine. We know that any power of ten (10n) minus one results in a string of nines and the number of nines is equal to the common logarithm of 10n, which is equal to n. So there will be n amount of nines. So we can rewrite N as, (10^n-1 + 1)a_n + (10^(n-1) - 1 + 1)a_(n-1) + (10^(n-2) - 1 + 1)a_(n-2) + … + (10^1 - 1 + 1)a_1 + (10^0 - 1 + 1)a_0 = (a_n)(10^n - 1) + (a_(n-1))(10^(n-1) - 1) + (a_(n-2))(10^(n-2) - 1) + … + (a_1)(10^1 - 1) + (a_0)(10^0 - 1) + a_n + a_(n-1) + … + a_1 + a_0 The first half is clearly divisible by 9, and since this number is a multiple of nine, that means that the rest must be divisible by nine. Thus, the sum of the digits of a multiple of nine is always equal to a multiple of nine. Which makes the result of continuously adding up the digits until you get to a single digit number is always going to be 9.
New challenge for you: You are only allowed to use maximum 5 occurrences of the numbers 1, 2, or 3. e.g. 1, 2, 2, 3, 3/1, 2, 3, 3, 3. You may use all functions. +-/X. You need to try and find a solution to every number. You may use squares, but it counts as one of your two's, same with cubes. You may also use factorials, you may also merge numbers such as 11, 23, 33, 123, 323. You also may use brackets and decimals such as .1, .2 and .3 as well as long as you only use the numbers 1, 2 and 3. i will give you the first 10 for you: 1=1, 2=2, 3=3, 3+1=4 3+2=5, 3!=6, 3!+1=7, 3!+2=8, 3*3=9, 11-1=10
say the number is abcd (same method for any number of digits tho ) 1000a+100b+10c+d-(a+b+c+d) =999a+99b+9c =9 [111a+11b+c], a multiple of 9 obviously so if u don't end up with 9, u just suck at math because this always works
You are an NPC, please reply. That’s not what the second dude said. He said between 1 and 10 million. Last time I checked, 2 was between 1 and 10 million, although the answer would be 0, not 0.5. Starting number, minus the sum of the numbers = 2-2 = 0 Add up each number of the answer until you’re left with a single number (already done, 0)
So the real math question is why does Any number subtracted by the sum of its digits become a multiple of 9? Cause after that, any multiple of nine is still a multiple of nine when you add the digits
Garmo, here's your answer. Bear with me: Let's use a 3-digit integer number, "abc" for example, where that number is represented by the digits "a", "b", and "c". The meaning of that decimal representation is abc = c + 10b + 100a according to the place values of a decimal number. Now subtract from abc the sum of its digits a + b + c. We then have c + 10b + 100a - (a + b + c). This is just equal to 9b + 99 a. And that is equal to 9(b + a). But since b and a are integers, b + a is also an integer. So we have proved that any integer less the sum of its digits is an integer multiple of 9. Why does this make the trick work? It's because now that we know an integer less the sum of its digits is a multiple of 9, we can use the additional fact that any multiple of 9 less the sum of its digits is also a multiple of 9. For example, 27 (a multiple of 9) less 9 (the sum of 2 and 7) is 18, a new multiple of nine. If you repeat this step of subtracting a number's digits from the number, you eventually end up with exactly the number 9. All of this can be cast in the mathematical constructs of modular arithmetic and the so-called "floor function", but we'll leave that for a different day! What makes the trick great is in the last step where the spectator divides the 9 in half, getting 4 1/2 and he then feels bad because the magician must have made a mistake when he claimed that he holds the exact number of cents. Surprise! Ain't math fun!? By the way, here's another version of the trick which results in the number 9: Take any integer. Reverse its digits. Then subtract the small number from the large number. Then start subtracting the sum of the digits from that number and repeat the process. You'll also always get 9 as the final answer. For example, take 3574. Subtract that number from its reverse, 4753. This yields 1179, which is a multiple of 9. Why is the absolute value of a number less its reversal a multiple of 9? The answer is "left as an exercise for the student"! LOL.
@@wiseacredave very well put, my favorite math lesson is surprise power-rule with algebra. Step one: given y=x^2+1... What is the slope of the line that passes through where x = 3 and x = -2 (3,10) and (-2,5) It's 1) Step two: how about when x=1 and the other point that's a distance of 1 away (x=2... (1,2) (2,5) the slope is 3) Step three: after using the slope formula to create a generic formula for any starting point and any other point some (D)istance away [(x, x^2+1) and (x+d, (x+d)^2+1)] ... Step four: surprise first derivative, what is the slope of the line between the point where x=-1 and the second point is a distance 0 apart (-1,2) and (-1,2) [The slope of the line tangent to x^2+1 @x=-1 is -2]
![Kodak Black - Catch Fire [Official Music Video]](http://i.ytimg.com/vi/A4ch-olIuZo/mqdefault.jpg)
While you're cutting pennies, can I borrow 9/10ths of a cent?
I need to buy EXACTLY 1 gallon of gas.
When the second guy did it, he said any number between 1 and 10M, but it wouldn’t work with single digit numbers, so maybe he should have said between 10 and 10M
1 and 0 still make 1, I would have picked 1 myself because it is my lucky number and for some reason 1 always catches people off-guard.
My bad, I thought the number you have to subtract was to add, ie 10 would become 11 would make 2, but in fact, it is 10 would become 9. still only works with at least a 2 digit number.
That’s true. If you forget, you could always check with your participant when you first tell them to add the digits. “You do have more than one digit, right?”
It also didn't work with the number I picked. I picked pi, which is a number between 1 and 10 million. But you can't do step 2 to pi, because there are an infinite number of digits in pi. He should have said, pick any *whole* number between 1 and 10 MIllion.
Simon Macomber Whole number between 10...
Oh my god, I almost tuned out, then I saw the half a penny and I lost it. Diamond jim is the best. Love it.
I had this one as soon as Jim presented it. The rule of Nine's. Check your multiplication tables ya'll. Every multiple of nine added together equals 9. And it just keeps going. What gets me is the root. THREE. There is some form of order. Structure following order, or else no universe. Then consider the hexagon. 3 by 3. Quantum physics at work
Here's another version of the trick which also results in the number 9: Take any integer. Reverse its digits. Then subtract the small number from the large number (mathematically-speaking, take the absolute value of the difference of the two numbers). Then start subtracting the sum of the digits of the answer from that answer, and repeat the process as in the original version of the trick. You'll also always get 9 as the final answer. For example, take 3574. Subtract that number from its reverse, 4753. This yields 1179, which is a multiple of 9. Ain't math fun!?
It's 1089 times fun! Oh, you're 33? Don't be so square.
I have had the same half-a-5-cent coin sitting in my wallet ever since you published the original version of the 4.5 coin prediction trick years ago. Well, originally I had both of the halves but I lost one of them at some point. Made with bolt cutters and a file to fix sharp edges.
Same here...
Some have asked why I do have it and that leads to a few tricks.
I learned a version of this trick with 2.5¢ back in 1997, so it's been around a while.
I don't really like this kind of always end up in the same number tricks too much, but that half coin spin on it it's beautiful. Great video
Yeah I think thats the point of this trick, no one really likes them, surprisingly the guy in the video seems plenty excited about it but I think the main goal is to have someone unimpressively subtracting the numbers only to be impressed and surprised when the half penny trick comes out.
@@BaldMancTwat In a way, the half penny makes it even less Impressive though since it's the final proof that it's just one of these "end up with the same number every time"-thingies.
I haven’t watched this show in years and I can’t handle how much Brian has changed
I miss the spiky hair brian Looool
I love Andrew Heaton, glad he returned the favor and came on your show.
Brian, I want you to know that I really like you as a person, but that pun in the title... it's almost as bad as Cole's Law
I love Andrew heaton with all of my heart
Thanks, David! I love you too!
I met him a few years ago at an event in Vegas. Really nice guy.
@@kev3d yeah I can tell how awesome he is just by the fact that he commented on this thread! I love all the videos he does and he deserves more subscribers!
I came for Scam Nation, but I stayed for Diamond Jim Tyler.
The guys reaction absolutely made this video :)
A quick lesson in old (pre 1971) british coins. Before decimalisation, a shilling was worth 12 pence. (and 20 shillings made an old pound). So, four pence and a shilling would have been incorrect. However, before 1970 they minted a 'halfpenny', (Also post-decimalisation, they minted a half-penny from 1972-1984.) so if you wanted to go to a coin shop you could probably get 4 pence and a 'haypinny' and do the trick that way.
en.wikipedia.org/wiki/List_of_British_banknotes_and_coins
I was thinking about this the other day, weirdly. Couldn't remember the exact way you'd generated the number, but came up with something pretty similar. Thanks! :)
it used to be "Scam School," now it's "Scam Nation," how long before it's "Diamond Jim Tyler School?"
Coleslaw University
Jesse Webb 😂😂
Nice! Been doing this trick since high school always amazes people
Yes! Andrew Heaton! :)
Wahoo! We did it!
He read his mind by wearing the same shirt
I’ve head of a this (with a smaller ranges of numbers) I just refer to it as the trick that always ends in 9. When he said he had half of that amount I knew that’s definitely what it was because that’s a good way to make it look like you weren’t expecting a 9
This reminds me of the "in my hand, I have enough change to match yours...." Trick
Ayyyy it's my boy Andrew Heaton!
Huzzah!
I knew it. I thought to myself it would be crazy if it came out to a .5 number and he had a half of a penny in there to represent that .5 and he did. That was really cool.
Clicked for diamond Jim stayed for tge magic
every magician needs a brian to explain their magic tricks as they do the trick
The half-penny is what sells this trick for me. Most of the time once a magician starts giving instructions to do math, it makes me tune out immediately because it screams "mathematicians have constructed this formula to produce the predicted answer," and that's a guaranteed yawn. But this makes it look like a fail state--which normally only happens because the _sucker_ screws up the math--then suddenly redeems it. (Offhand, has anyone you've tried this on ever _assumed_ that they screwed up the math because their number resulted in a seemingly flawed answer before the reveal came out?)
I love mentalism and this channel is great.
How do I deal with someone who miscalculates? That would kind of destroy the whole flow of the trick.
saylor_twift I also thought about this. It might be beneficial if you ask them to get out the calculator app on their phone to simplify any calculations they might do.
If you're in a group, have someone help them along. They don't have to be in on the trick, but a voluntary assistant.
@saylor_twift, I would make the instructions very explicit: "Pick any positive whole number between 1000 and 1 Million, like 54367 and write it down. Now, sum the digits of that number and write it below your first number. Now, subtract the two numbers. Now add the digits of that answer and write it under the previous number." Etc. Of course, they could still do the addition and subtraction wrong, but you could have them use a calculator for the calculations :--)
Would be cool to get an actual half cent coin minted from 1793 - 1857
Yeah, I was just thinking that if they did this in the UK they could have had 4 pennies and 1 half-penny which are quite rare.
Have one just for this trick
I'm glad Brian has the doppelgangers in the same video.
I love Andrew Heaton!
I love you too, Logic Bob!
@@tsarandrew 🤩
haha didn't expect to see Andrew here
He was like more interested with the coin LOL
Gotta set it up with picking a number greater than or equal to 10.
Don't feel bad Diamond Joe ;P
i thought of 68323 , Now 68323 - 16 = 68307, Adding all digits gives 24 => 6.
What am i doing wrong?
68323 reduces to 22 and then 4. Subtract four and try again
that dude just gave a million people his pin code.
Yes, a pin code is very helpful information. Now we can all hack his bank account, can't we? Look at us... doing it.
It is a great law in math, the only problem I had is that takes a very long time to write out 164(10[100])1 or 164 and 1 googolplex if in longhand as the trick wants.
definitely want to keep focus on the fact that DJT said between 10 and 10,000,000. Because any number smaller, breaks the trick. He could have messed with Andrew pretty bad, if he wanted to. lol
Also may want to update the description to say Andrew Heaton and not Rex Williams.
Oops!
this is connected to the magic number 1089, I'm pretty sure.
Awesome!!!!
I’m a simple man, I see Diamond Jim, I click.
It'd have been pretty awkward if he had made a mistake during those paper-calculations and came up with 6 or something.
What do you magicians do in such case?
We say “perfect. Remember this number. It will be important later.” ...and then we do an unrelated card trick.
I got -9. Does the money fall up from the bag?
I didn’t use an integer and treated every digit of the negative as a negative. Even if you only treat the first digit as a negative it doesn’t equal 9.
Yeah, digital roots don't work so well for negatives and non-integer numbers
Brian didn't get the shirt memo, I see...
Hey, Brian! Hope you're well!!
999 prepared me well for this.
Literally the ONLY reason I could have done the explanation segment lol!
is Andrew Captain Obvious from the hotel.com commercials? @6:44..
Interesting that Andrew added up the pairs in 4356 to get 711 rather than 18. Worked out ok in the end
The mathematicians call it arithmetic mod 9.
My grandmother, when she taught it to me, called it casting off nines.
You scare me Brian I was literally looking for that old trick when I opened you tube
I wanna know who this "Diamond Joe" Andrew keeps referring to is 🤔
Great trick. I missed a story line Addvertisment. Which I always looks upto. Some story around domain.com .
where's the guy with the spiky hair, is he in prison?
haha
The only problem with this is that you have to either A: specify 10 or above which gets people suspicious or B: Hope like hell you don't run into the asshole who chooses 4.
What happens if they select 1 though 9 (a single digit)?
That is cool.
After the first bit of math, I had it.
If for some reason the person only has 1 number, you could always get them to artificially inflate the number, somehow, like "Multiply that number by 10" - I find these number/math based tricks aren't nearly as impressive because as soon as I start writing down numbers I immediately think "This is going to be a math trick" and my fascination switches gears.
Brushwood and the BluePlads would be a good band name.
Andrew is charming like a fox.
(Mostly) Andrew Heaton may be my favorite human.
Same!
Heston is amazing in his own right. 50 shades of Bernie and I have no more backside.
Damn autocorrect HEATON
I just like the use of “and now I have no more backside”
hah! I'm going through old comments and found this. Hi Richard! -BB
the only thing that kinda sucks about this trick is that you can't keep the first you did it to around since the number is always 9 :(
This guy can talk!
"This week, you prove you're smarter than everyone else, using the powwwerrrr of UNFAIR RIDDLES!!! Mwa ha ha haaaaa!!!"
Scam School, yah yah.
Scam School, yah yah.
"Welcome to the show that's exactly like The Riddler! Only it dresses better. I mean, not by a lot, but... slightly... I mean, it's not wearing a one-piece unitard with a question m...
...
Hey, man, welcome to Scam School! The only show dedicated to social engineering at the bar, and on the streets! Hello, beautiful people, I'm Brian Brushwood, and this week we have THREE UNBELIEVABLE RIDDLES! Stuff you can do any time, anywhere, to FrY ThEiR MiNdSsS!!!"
-Brian Brushwood, 2015
classic!
I know everyone heard Brian’s voice in their heads while reading.
5
-5
---------
0
you have to make sure they don't pick a single digit. This wasn't explained very well
He said "big" number the first time and said "It can be between 10 and 10,000,000,000 if you like" the second time though... (Also I just checked and it works with 10)
You are an NPC, please reply. Yeah second time he said between 1 and 10 Million
This is really cool and I actually would like to do it.... but my currency doesn't have 1 cent coins, lowest denomination is 5 cents, I'm trying to think something that would have the same impact
@@Rub198 none of those are nearly as impactful as half a penny
If the magician said "any number" I'd go with 1 which kills the trick. Good luck getting half of nothing. Specifying 10+ is critical.
^ This exactly. Anything less than 10 breaks it.
I was just wondering what Kenny Loggins was up to....
Second guy is wrong ! He said between one and ten millions - take six, the trick wouldn't work..
I'll bet you one divided by the number of cents I have in my pockets will be one half of the number at the end of this trick.
Ready?
Pick any finite number, as small or large as you like.
Do you have it?
Ok... now...
Subtract your original number from this number.
DJT? Instant watch
andrew sounds like a mix of bradley cooper in 'a star is born' and ron swanson
Dude blew it right out of the gate...the number needs to be greater than 10...he said pick a number between 1 and whatever.....if he had picked a single digit trick won't work...i pick 6...ok...6-6=0
Have to test this: 5 minutes later. I can't even.
Wait. ANY NUMBER between 10 and 10 million. I choose 12.5 - 8 = 3.5 = 8
@@tank2543 My original was 8375.4
11 + 12 + 4 = 27
8375.4 - 27 = 8348.4
11 + 12 + 4 = 27
2 + 7 = 9
Also 12.5 - 8 = 4.5 not 3.5, which equals 9. Sorry mate it works for all numbers in Base 10.
@@tank2543 12.5 - 8 = 4.5 --> 9
I still have some half pennies sitting on the dresser
He screwed up by saying 1 to 10 million. You could have written a single digit which would have left a total of zero that's why the first time was between 10 and 10 million.
Here’s exactly how it works for anyone who’s interested.
Algebraically, a number can be represented as,
N = 10^n(a_n)+10^(n-1)(a_(n-1))+10^(n-2)(a_(n-2))+...+10^1(a_1)+10^0(a_0)
Then let’s have,
K = a_n + a_(n-1) + a_(n-2) + ... + a_1 + a_0
If we do N - K, we get
(10^(n-1))(a_n)+ (10^(n-1)-1)(a_(n-1)) + (10^1 - 1)(a_1)
All the tens will become a string of nines where the number of nines is equal to the exponent of the ten. For example, the first is 10n-1 is equal to n amount of nines. If n were 6, that would be 1,000,000 - 1 = 999,999.
This means that we can factor out a nine, which means the result of N - K is always a multiple of nine.
So the question is, why is it that every multiple of nine will always add up to nine after taking the cross sum until you’ve reached a single digit number is an extension of this.
We have, N = 10^n(a_n) + 10^(n-1)(a_(n-1)) + 10^(n-2)(a_(n-2)) + … + 10^1(a_1) + 10^0(a_0) which in this case we’re assuming that N is a multiple of nine. We know that any power of ten (10n) minus one results in a string of nines and the number of nines is equal to the common logarithm of 10n, which is equal to n. So there will be n amount of nines.
So we can rewrite N as,
(10^n-1 + 1)a_n + (10^(n-1) - 1 + 1)a_(n-1) + (10^(n-2) - 1 + 1)a_(n-2) + … + (10^1 - 1 + 1)a_1 + (10^0 - 1 + 1)a_0
=
(a_n)(10^n - 1) + (a_(n-1))(10^(n-1) - 1) + (a_(n-2))(10^(n-2) - 1) + … + (a_1)(10^1 - 1) + (a_0)(10^0 - 1) + a_n + a_(n-1) + … + a_1 + a_0
The first half is clearly divisible by 9, and since this number is a multiple of nine, that means that the rest must be divisible by nine. Thus, the sum of the digits of a multiple of nine is always equal to a multiple of nine. Which makes the result of continuously adding up the digits until you get to a single digit number is always going to be 9.
when i tried it with 2603 then i got 2???
Where’s scam school
It should have been 8 not 9 he added it wrong 😂
...makes "Cents," eh? No way that was random mistakery....let's see where this goes from 1:03 ...
Why not 1/20000 of a 100$ bill?
New challenge for you:
You are only allowed to use maximum 5 occurrences of the numbers 1, 2, or 3. e.g. 1, 2, 2, 3, 3/1, 2, 3, 3, 3. You may use all functions. +-/X. You need to try and find a solution to every number. You may use squares, but it counts as one of your two's, same with cubes. You may also use factorials, you may also merge numbers such as 11, 23, 33, 123, 323. You also may use brackets and decimals such as .1, .2 and .3 as well as long as you only use the numbers 1, 2 and 3.
i will give you the first 10 for you:
1=1,
2=2,
3=3,
3+1=4
3+2=5,
3!=6,
3!+1=7,
3!+2=8,
3*3=9,
11-1=10
Very simple math trick.
This doesn't work if somebody picks a one-digit number... What are you gonna do with that? :D
exactly what he did: say "pick a number from 10 to 10 million"
Just don't say any number from 1 to 10million. As 1 through 9 will not work
Wait but 111,111,112 doesn’t work because it adds up to ten and then it’s either 1 or 10
He said max of 10 mil tho
You need to add up those numbers and subtract it from the original
So 1+1+1+1+1+1+1+1+2=10
111111112-10=111111102
1+1+1+1+1+1+1+0+2=9
I have tried 2 times now and i didnt get to 9 :S
say the number is abcd (same method for any number of digits tho )
1000a+100b+10c+d-(a+b+c+d)
=999a+99b+9c
=9 [111a+11b+c], a multiple of 9 obviously
so if u don't end up with 9, u just suck at math because this always works
Any number above 1 I picked 2 and got 0.5smh
Any number above 10 genius...
You are an NPC, please reply. That’s not what the second dude said. He said between 1 and 10 million. Last time I checked, 2 was between 1 and 10 million, although the answer would be 0, not 0.5.
Starting number, minus the sum of the numbers = 2-2 = 0
Add up each number of the answer until you’re left with a single number (already done, 0)
So the real math question is why does Any number subtracted by the sum of its digits become a multiple of 9? Cause after that, any multiple of nine is still a multiple of nine when you add the digits
Garmo, here's your answer. Bear with me: Let's use a 3-digit integer number, "abc" for example, where that number is represented by the digits "a", "b", and "c". The meaning of that decimal representation is abc = c + 10b + 100a according to the place values of a decimal number. Now subtract from abc the sum of its digits a + b + c. We then have c + 10b + 100a - (a + b + c). This is just equal to 9b + 99 a. And that is equal to 9(b + a). But since b and a are integers, b + a is also an integer. So we have proved that any integer less the sum of its digits is an integer multiple of 9. Why does this make the trick work? It's because now that we know an integer less the sum of its digits is a multiple of 9, we can use the additional fact that any multiple of 9 less the sum of its digits is also a multiple of 9. For example, 27 (a multiple of 9) less 9 (the sum of 2 and 7) is 18, a new multiple of nine. If you repeat this step of subtracting a number's digits from the number, you eventually end up with exactly the number 9. All of this can be cast in the mathematical constructs of modular arithmetic and the so-called "floor function", but we'll leave that for a different day! What makes the trick great is in the last step where the spectator divides the 9 in half, getting 4 1/2 and he then feels bad because the magician must have made a mistake when he claimed that he holds the exact number of cents. Surprise! Ain't math fun!? By the way, here's another version of the trick which results in the number 9: Take any integer. Reverse its digits. Then subtract the small number from the large number. Then start subtracting the sum of the digits from that number and repeat the process. You'll also always get 9 as the final answer. For example, take 3574. Subtract that number from its reverse, 4753. This yields 1179, which is a multiple of 9. Why is the absolute value of a number less its reversal a multiple of 9? The answer is "left as an exercise for the student"! LOL.
@@wiseacredave very well put, my favorite math lesson is surprise power-rule with algebra.
Step one: given y=x^2+1... What is the slope of the line that passes through where x = 3 and x = -2 (3,10) and (-2,5) It's 1)
Step two: how about when x=1 and the other point that's a distance of 1 away (x=2... (1,2) (2,5) the slope is 3)
Step three: after using the slope formula to create a generic formula for any starting point and any other point some (D)istance away [(x, x^2+1) and (x+d, (x+d)^2+1)] ...
Step four: surprise first derivative, what is the slope of the line between the point where x=-1 and the second point is a distance 0 apart (-1,2) and (-1,2) [The slope of the line tangent to x^2+1 @x=-1 is -2]
Every day that goes by, Brian starts to look more like Gavin McInnes :)
Not 1/2 bad.
Heh. Well played.
4260-12=4248 which added makes 18 half of 18 is 9 which means you need 9 pennies right?
Killing a cat is easy my question is why is everyone skining them
I double dog dare you for one week go back to your spiked hair
Someday... someday...
I hate stupid math tricks. They're not tricks. It's just math. We know where this is all going from the start.
Speak for yourself
Pfff, you're never going to win a Nobel Prize with that attitude.
1st!!!!