21:37 Well, you got a 3 and 663 is divisible by 3, which gets you 221. Prime factors are 13 x 17. Easy enough to get to 17 with 25 - 8 but getting to 13 isn't really possible; getting to 39 however is, so just put the 3 back and do... 100 / 50 = 2 75 + 3 = 78 78 / 2 = 39 25 - 8 = 17 39 x 17 = 663 ...I suppose the divisible by 3 was obvious, but I assume getting the prime factors of 221 would have taken most people quite a while... maybe I'll find some time in the future to do some tutorial videos for things like this.
It really shouldn't have taken me so long to figure out that 221 = 15^2 - 2^2 = (15+2)(15-2) Anyways, it's really funny to see the players solving a trivial one and just... waiting
5:03 ... 25 × 10 = 250; 8 × 8 = 64; 250 + 64 = 314; 6 ÷ 2 = 3; 314 + 3 = 317 I got the 186, I wrote it as a reply to a comment somewhere else around here. 17:34 ... 50 × 8 = 400; 9 × 4 = 27; 400 - 27 = 373; 373 - 8 = 365; 365 + 3 = 368 21:42 ... was doable, according to the webpage I found that has a solver; I know when I'm out of my league. Our courteous host Björn left that bit out... or else the show had to cut it for time. 25:26 ... 8 - 2 = 6; 6 × 6 =36; 36 × 10 = 360; 5 × 5 = 25; 360 - 25 = 335 I did get the 512, but it was the same as the players. You can assume that I missed all the rest.
4:43 Rachel deliberately chooses the most difficult solution in order not to embarrass the candidates. (6/2)+10 also gets you 13. It was quite hard not to see that.
In the first round of Monday, I saw both contestants' solutions, but one can use factoring (23 x 7 x 2 = 322) to solve it as a "five small": 10 x 4 = 40 40 + 6 = 46 10 - 3 = 7 46 x 7 = 322 And I also had this similar solution to Rick: 100 + 6 = 106 106 x 3 = 318 318 + 4 = 322 Finally, I had this solution: 100 - 10 - 10 = 80 80 x 4 = 320 6 / 3 = 2 320 + 2 = 322 In the second round, I saw Rick's solution, but also had these solutions: 25 + 8 = 33 33 x 4 = 132 132 + 9 = 141 9 + 6 = 15 15 x 8 = 120 120 + 25 = 145 145 - 4 = 141 8 + 4 = 12 12 x 9 = 108 108 + 25 = 133 133 + 8 = 141 In the third round, I got Rachel's solution, except she did it in a complex way to hide how easy it was. She could have done the following: 6 / 2 = 3 10 + 3 = 13 25 x 13 = 325 325 - 8 = 317 Another thing she could have done was this: 25 x 10 = 250 8 x 8 = 64 250 + 64 = 314 6 / 2 = 3 314 + 3 = 317 Finally, you can solve it as a "five small" in this way: 10 x 8 x 8 = 640 640 - 6 = 634 634 / 2 = 317 In the final round, I saw both contestants' solution, but I was surprised they didn't go for other easy solutions, like the following: 100 - 4 = 96 9 + 1 = 10 96 x 10 = 960 100 + 50 + 9 + 1 = 160 160 x 6 = 960 50 - 9 - 1 = 40 40 x 6 x 4 = 960 I'll post my solutions for Tuesday's game in another comment below this.
In the first round of Tuesday, I had these "five small" solutions from factoring (31 x 3 x 2 = 186): 8 x 3 = 24 24 + 7 = 31 31 x 6 = 186 8 x 7 = 56 56 + 6 = 62 62 x 3 = 186 And these easy solutions with the 25: 25 x 7 = 175 175 + 6 + 5 = 186 8 - 7 = 1 25 + 5 + 1 = 31 31 x 6 = 186 25 - 7 = 18 8 + 5 = 13 13 - 3 = 10 18 x 10 = 180 180 + 6 = 186 In the second round, I saw Rachel's solution, but I also had this one based on factoring (29 x 11 x 2 = 638): 50 + 8 = 58 9 x 3 = 27 27 + 9 = 36 36 - 25 = 11 58 x 11 = 638 I couldn't see any other solutions, though. In the third round,. I saw Rick's solution and this other one: 75 x 6 = 450 450 + 5 = 455 455 x 2 = 910 10 / 10 = 1 910 - 1 = 909 Again it's the only other one I could spot, so either I'm having a moment of mental dullness here or these are some seriously difficult problems. In the final round, I saw Rachel's solution. However, Rick was very nearly there with his solution. He should have done this: 4 x 3 = 12 25 - 12 = 13 75 x 13 = 975 975 + 5 = 980 Another easy way is: 25 x 8 = 200 200 - 4 = 196 196 x 5 = 980 Finally, I also had this: 75 - 5 = 70 25 - 8 - 3 = 14 70 x 14 = 980
In the first round on Wednesday, I saw Rick's solution but also factored (11 x 5 x 3 x 2^2 = 660) for these solutions: 50 x 2 = 100 100 + 7 + 3 = 110 110 x 6 = 660 8 - 3 = 5 50 + 5 = 55 55 x 6 x 2 = 660 50 - 6 = 44 8 + 7 = 15 44 x 15 = 660 In the second round, I saw Rachel's solution, and also had these (the first one was so easy to spot I saw it before the clock started): 50 x 9 = 450 450 - 75 - 8 = 367 3 / 3 = 1 367 + 1 = 368 50 - 3 = 47 75 - 3 = 72 72 / 9 = 8 47 x 8 = 376 376 - 8 = 368 75 + 50 = 125 125 x 9 = 1125 1125 + 3 = 1128 1128 / 3 = 376 376 - 8 = 368 In the third numbers round, I saw Rick's solution and also had these: 25 x 6 x 3 = 450 8 / 4 = 2 7 x 2 = 14 450 - 14 = 436 8 - 7 = 1 25 - 1 = 24 24 x 6 x 3 = 432 432 + 4 = 436 And this one from factoring (109 x 2^2 = 436): 25 - 8 = 17 17 x 6 = 102 102 + 7 = 109 109 x 4 = 436 In the fourth round, I had the unusual pleasure of beating Rachel in a numbers round and doing it in the 30 seconds. The following is the only way I have seen, however, so it's no reflection on her that she didn't get it: 75 + 3 = 78 78 x 50 = 3900 25 - 8 = 17 3900 x 17 = 66300 66300 / 100 = 663 Admittedly, you can do 100 / 50 = 2 and divide by 2, so you don't need to go into the tens of thousands, but when you have a four-large game why not have some fun with it? I got this by factoring (17 x 13 x 3 = 663). 78 is twice 39, so if you add 3 to 75, then divide it by 2 (or break it up as I did), then you'll get 39 x 17 = 663.
In the first round on Thursday, I saw Peter's solution, and also had these solutions by factoring (13 x 5 x 2^2 = 260): 5 x 2 = 10 75 - 10 = 65 3 + 1 = 4 65 x 4 = 260 75 / 3 = 25 25 + 1 = 26 26 x 5 x 2 = 260 8 x 3 = 24 75 - 24 = 51 51 + 1 = 52 52 x 5 = 260 8 + 3 = 11 11 x 2 = 22 75 - 22 = 53 53 - 1 = 52 52 x 5 = 260 In the second round, I saw Peter's method of getting 67 and also had this one: 10 + 2 = 12 12 x 6 = 72 72 - 5 = 67 67 x 5 = 335 And I had these related solutions: 8 x 5 = 40 40 - 6 = 34 34 x 10 = 340 340 - 5 = 335 6 x 5 = 30 8 / 2 = 4 30 + 4 = 34 34 x 10 = 340 340 - 5 = 335 In the third numbers round, I saw both contestants' solutions and also had these solutions: 100 / 4 = 25 25 x 7 = 175 175 + 8 = 183 183 x 4 = 732 100 - 8 = 92 9 - 7 = 2 92 x 4 x 2 = 736 736 - 4 = 732 In the final numbers round, I saw Colin's solution, and also had these ones: 10 - 4 = 6 9 x 7 x 6 = 378 378 + 1 = 379 10 x 9 = 90 90 + 1 = 91 91 x 4 = 364 364 + 8 + 7 = 379 I'll come back and finish Friday later.
In the first numbers round on Friday, I saw Peter's solution, of course. It's so good that I'm almost tempted to just leave it, but in the interests of having something else to say I also came up with these alternatives: 8 + 4 = 12 12 x 6 = 72 72 - 7 - 1 = 64 64 x 8 = 512 7 + 6 + 1 = 14 14 x 4 = 56 56 + 8 = 64 64 x 8 = 512 8 + 4 = 12 12 x 7 x 6 = 504 504 + 8 = 512 In the second round, I'm surprised it took Rachel so long to come up with the solution. I saw hers in the 30 seconds, as well as this one: 8 x 5 = 40 40 + 2 = 42 25 - 5 = 20 42 x 20 = 840 840 + 9 = 849 In the third round, with the 8 on the board it was odd neither Rachel nor the contestants tried to come at the target via 390, which can be done in the following way: 9 + 4 = 13 13 x 6 x 5 = 390 390 - 8 = 382 And I also had these two related solutions: 8 - 1 = 7 9 x 7 x 6 = 378 378 + 4 = 382 8 x 6 = 48 48 - 5 - 1 = 42 42 x 9 = 378 378 + 4 = 382 In the final numbers round, I beat Rachel to the solution again, getting my solutions well within the 30 seconds, but I was helped by working out the factors of 638 (29 x 11 x 2 = 638) only yesterday, because this was the target of the second numbers round on Tuesday's show. My solutions based on factoring are: 25 - 6 = 19 19 x 3 = 57 57 + 1 = 58 8 + 3 = 11 58 x 11 = 638 6 + 1 = 7 7 x 3 = 21 21 + 8 = 29 25 - 3 = 22 29 x 22 = 638 8 x 3 = 24 6 - 1 = 5 24 + 5 = 29 25 - 3 = 22 29 x 22 = 638
For Monday: ---------------------- In the first round, the contestants' solutions are obvious. Apart from the solutions, there are several ways to obtain the target: 100 + 6 = 106 3 x 106 = 318 318 + 4 = 322 100 + 10 = 110 3 x 110 = 330 10 + 4 = 14 14 - 6 = 8 330 - 8 = 322 4 x 10 = 40 40 - 3 = 37 37 x 6 = 222 222 + 100 = 322 100 - 10 - 10 = 80 80 x 4 = 320 6 / 3 = 2 320 + 2 = 322 Besides, it is noticed that 322 = 2 x 7 x 23, so it is possible to obtain the target with the small numbers: 4 x 10 = 40 40 + 6 = 46 10 - 3 = 7 46 x 7 = 322 The second round is another easy round. Rick's solution is immediately obtained before the clock started. In addition, there are some alternate solutions found: 25 - 6 = 19 19 x 8 = 152 8 / 4 = 2 9 + 2 = 11 152 - 11 = 141 25 - 8 = 17 17 x 8 = 136 9 - 4 = 5 136 + 5 = 141 25 + 8 = 33 33 x 4 = 132 132 + 9 = 141 Since 141 = 3 x 47, one way to obtain the target with factoring is: 9 x 8 = 72 72 - 25 = 47 6 x 4 = 24 24 / 8 = 3 47 x 3 = 141 For the third round, it is a bit tricky because all small numbers are even. While there are many ways to get one-away (either 316 or 318), a simpler way to Rachel's solution is: 6 / 2 = 3 10 + 3 = 13 13 x 25 = 325 325 - 8 = 317 It seems that the only way to obtain the target is making 325. For the last round, the contestants' solution can be obtained without any effort. Apart from that, there are a couple of ways to obtain the target using factoring: 100 + 50 + 9 + 1 = 160 160 x 6 = 960 50 - 9 - 1 = 40 40 x 4 x 6 = 960 Besides, there are several other intuitive ways: 9 + 1 = 10 10 x 100 = 1000 1000 - 50 = 950 950 + 4 + 6 = 960 100 - 4 = 96 9 + 1 = 10 96 x 10 = 960 For the other days, I will post in separate comments.
For Tuesday: --------------------- The first round is easy and there are lots of ways to obtain the target. I was expecting the contestants could get this one: 25 x 7 = 175 6 + 5 = 11 (or 8 + 3 = 11) 175 + 11 = 186 Apart from Rulus's solution, there are several ways to obtain the target based on factoring (186 = 31 x 2 x 3): 25 + 6 = 31 5 + 8 - 7 = 6 31 x 6 = 186 25 + 6 = 31 7 - 5 = 2 31 x 2 x 3 = 186 8 x 7 = 56 56 + 6 = 62 62 x 3 = 186 3 x 8 = 24 24 + 7 = 31 31 x 6 = 186 Besides, there are several other alternatives, with the first one similar to Rulus's solution: 25 x 8 = 200 5 - 3 = 2 2 x 7 = 14 200 - 14 = 186 25 + 5 - 7 = 23 23 x 8 = 184 6 / 3 = 2 184 + 2 = 186 For the second round, since 638 = 2 x 11 x 29, there is one way to obtain the target with factoring: 50 + 8 = 58 9 x 3 = 27 9 + 27 = 36 36 - 25 = 11 11 x 58 = 638 For the third round, I get Rick's straight-forward solution, but I cannot find any alternative for this one. For the fourth round, it is noticed that 980 = 2 x 2 x 5 x 7 x 7, in addition to Rachel's solution, there are several ways to obtain the target with factoring: 75 - 5 = 70 25 - 8 - 3 = 14 14 x 70 = 980 25 x 8 = 200 200 - 4 = 196 196 x 5 = 980 25 + 3 = 28 8 x 5 = 40 75 - 40 = 35 28 x 35 = 980
For Wednesday: -------------------------- For the first round, there are lots of ways to obtain the target. Apart from Rick's obvious solution, I got several alternatives using factoring: 50 x 2 = 100 100 + 7 + 3 = 110 110 x 6 = 660 50 + 3 - 8 = 55 55 x 6 x 2 = 660 8 x 2 = 16 50 + 16 = 66 7 + 3 = 10 66 x 10 = 660 For the second round, I also noticed that 368 = 46 x 8, so I got Rachel's solution within the 30 seconds. Apart from Rachel's solution, I got one alternative: 50 x 9 = 450 3 / 3 = 1 450 + 1 = 451 451 - 75 - 8 = 368 The third round is another easy round. It is easy to notice that 436 = 109 x 4, which means one way to obtain the target is to make 109, and it is doable as: 7 x 6 = 42 42 - 8 = 34 25 x 3 = 75 34 + 75 = 109 109 x 4 = 436 Besides, it is possible to achieve the target from 450 as: 25 x 6 x 3 = 450 8 / 4 = 2 7 x 2 = 14 450 - 14 = 436 For the fourth round, I got the solution using factoring, as 663 = 13 x 3 x 17: 25 - 8 = 17 75 + 3 = 78 100 / 50 = 2 78 / 2 = 39 17 x 39 = 663
For Thursday: ---------------------- The first round is an easy round. I get Rick's solution in almost a second. Apart from the contestants' solutions, I get several alternatives using factoring: 8 + 2 = 10 (or 5 x 2 = 10) 75 - 10 = 65 3 + 1 = 4 (or 5 - 1 = 4) 65 x 4 = 260 75 / 3 = 25 25 + 1 = 26 26 x 5 x 2 = 260 3 x 8 = 24 75 - 24 + 1 = 52 52 x 5 = 260 For the second round, it is easily spotted that 335 = 67 x 5, so I got the same solution as Peter's. Besides, I found similar alternatives: 2 + 8 = 10 6 x 10 = 60 60 + 5 = 65 65 x 5 = 325 325 + 10 = 335 6 x 10 = 60 60 + 8 - 2 = 66 66 x 5 = 330 330 + 5 = 335 The third round is another easy round. I got Peter's solution after Rachel saying the target. Apart from the contestants' solutions, I get one alternative using factoring: 9 x 8 = 72 72 + 7 + 4 + 100 = 183 183 x 4 = 732 For the fourth round, apart from Colin's easy solution, I obtain an alternative instead: 10 + 4 = 14 14 - 8 = 6 6 x 7 x 9 = 378 378 + 1 = 379
For Friday: ----------------- For the first round, since 512 = 2^9 is a 101 fact in computer science, so I got an alternative solution immediately: 7 - 6 + 1 = 2 2 x 4 x 8 x 8 = 512 For the second round, I got Rachel's solution in a few seconds, since it is easily spotted that 850 = 34 x 25. However, I cannot find any alternative for this one. For the third round, since I like to make number divisible by 3 and 9, so apart from Rachel's solution, I found another way to achieve the goal, based on the solution I found for 379 from previous day: 8 - 1 = 7 6 x 7 x 9 = 378 378 + 4 = 382 For the final round, I found Rachel's solution after a few tries. Besides, I found that 638 = 2 x 11 x 29. Therefore, a couple of alternatives by factoring are: 6 + 1 = 7 3 x 7 = 21 21 + 8 = 29 25 - 3 = 22 29 x 22 = 638 3 x 8 = 24 24 + 6 - 1 = 29 25 - 3 = 22 29 x 22 = 638 25 - 6 = 19 19 x 3 = 57 57 + 1 = 58 8 + 3 = 11 58 x 11 = 638
Sorry everyone, I didn't have the time to upload daily this week... so grab a snack, this is the whole week in one video. 😉
Thank you for doing these videos!! ❤
My brain exploded when Rufus did his 186, as I was too lazy and did 25*7+8+3
Same, but 5 + 6 instead of 8 + 3
I did 25 × 6 + (8 × 3) + 7 + 5
21:37 Well, you got a 3 and 663 is divisible by 3, which gets you 221. Prime factors are 13 x 17. Easy enough to get to 17 with 25 - 8 but getting to 13 isn't really possible; getting to 39 however is, so just put the 3 back and do...
100 / 50 = 2
75 + 3 = 78
78 / 2 = 39
25 - 8 = 17
39 x 17 = 663
...I suppose the divisible by 3 was obvious, but I assume getting the prime factors of 221 would have taken most people quite a while... maybe I'll find some time in the future to do some tutorial videos for things like this.
Oh my god 38 minutes! This is amazing
Outstanding! Peter Burke is unbelievably smart. Dethroning Rick Singh is a herculean task. Respect to you Sire!
I’m pleased to see Colin solve one.
Now I’d like to see Jimmy Carr solve one
As a Blue Jays fan, it was a great surprise to see Colin in the sweater on the Dec.8 episode
Thank you!
What happened to Susie? I didn't see her in some moments.
Another 638 comes from its factorization 22*29. [25-3] x [3*8 + 6 - 1]
14:00 : [980]
4 + 8 = 12 ;
12 * 75 = 900 ;
3 * 25 = 75 ;
900 + 75 + 5 = 980.
NB : No Susie Dent ? 😕
How was 186 so complicated, even in the answer given by the guest? 25*7=175. 6+5=11. Add em.
33:45 - I got this in about 10 seconds. Seemed natural to use the x2 to make the 25 more useful.
Yeah, for a brief, shining moment I was smarter than Rachel !
The first one can be done with only the small ones
(10*4+6)*(10-3)
For 186:
(with 25, 7, 8, 5, 3, 6)
25 × 7 = 175
175 + 8 + 3 = *_186_*
512 was so easy, i literally immediately was 8³; you simply have to know your numbers
What word does Rachel say at around 18:53? "And the 7 and the 4, you have an EASOB(???)"
"you haven't used them"
@@bjoern.gumboldt Thanks!
25*10 = 250
8*8 = 64
6/2 = 3
250 + 64 + 3 = 317
That’s how i did that one lol
For 980 arund 14:00, I did:
75+3=78,
78*25=1950,
1950*4=7800
7800/8=975
975+5=980
...needless to say I felt a bit silly when Rachel pulled out 49*20 😅
could also do 13 saving the 5 with 8+4=12, 25-12 = 13 ... 13*75=975+5. but i like your way better
For the 335 at 25:00 or so, for those of us who don't know our x67 multiplication tables: 335=((5x6)+(8/2))x10-5
Thursday:
260:
8 + 2 = 10 (or 5 * 2 = 10)
75 / 3 = 25
25 + 1 = 26
10 * 26 = 260
8 * 3 = 24
75 - 24 + 1 = 52
52 * 5 = 260
75 - 1 = 74
74 * 3 = 222
8 * 5 = 40
222 + 40 - 2 = 260
335:
6 + 2 = 8
8 * 8 * 5 = 320
320 + 10 + 5 = 335
5 * 6 = 30
8 / 2 = 4
30 + 4 = 34
34 * 10 = 340
340 - 5 = 335
732:
Peter and Rick found the most obvious solutions, I also found this one by factoring:
9 * 8 = 72
100 + 72 + 7 + 4 = 183
183 * 4 = 732
379:
10 - 4 = 6
9 * 7 * 6 = 378
378 + 1 = 379
Just doing the ones they didn't get:
317:
10/2=5
5+8=13
13x25=325
325-8=317
186:
8x25=200
5x3=15
7-6=1
15-1=14
200-14=186
980:
25-8-4=13
13x75=975
975+5=980
663:
75x8=600
600+50=650
100/25=4
4x3=12
650+12=662 (1 away)
100 / 50 = 2
75 + 3 = 78
78 / 2 = 39
25 - 8 = 17
39 x 17 = 663
I did 980 with the following:
75x3=225
225-25=200
200-4=196
196*5=980
For 322:
(with 100, 10, 6, 10, 4, 3)
3 × 100 = 300
300 + 6 + 10 = 316
10 - 4 = 6
316 + 6 = *_322_*
14:13 (8+4)x75=900 + (3x25)+5
980 in a very very crazy way - and I can't believe I got it in 30 sec
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75 - 5 = 70
25+3 = 28
8/4 = 2
70/2 = 35. 35*28 = 980
Or 75×(25-4×3)+5 in an easier way - from my point of view...
I got the last one before Rachel :)
980 was for me 25 - (3x4) = 13 x 75 = 975 +5 = 980 (or simply said get 13 without using the 5 which obviously exclude 8 + 5)
For the 663 at 21:10 or so, best I could get was 662. 662 = (75x8)+(3x(100/25))+50. Did anyone get 663?
368 is for me 9 * 50 = 450 - 75 = 375 - 8 = 367 & 3/3 = 1 & 367 + 1 = 368; which i saw immediately
It really shouldn't have taken me so long to figure out that 221 = 15^2 - 2^2 = (15+2)(15-2)
Anyways, it's really funny to see the players solving a trivial one and just... waiting
317 = (25x10)+(8×8)+(6/2)
= 250 + 64 + 3
Same
Supporting Richard Osman to be the new host
436 is 3*6*25 = 450 & (8/4)*7 = 14 & 450 - 14 = 436
186 seemed quite easy. Could have gone
25x7 = 175
175+8+3 = 186
335
50x6=300
5x5=25
300+25=32 +8+2 = 335
35:30 My 382 is simpler: 8-1=7; 7*6=42; 42*9=378; 378+4=382
i got the 638 at the end differently
25 + 3 = 28 & 3 x 8 - 1 = 23 & 28*23 = 644 -6 is indeed 638
5:03 ... 25 × 10 = 250; 8 × 8 = 64; 250 + 64 = 314; 6 ÷ 2 = 3; 314 + 3 = 317
I got the 186, I wrote it as a reply to a comment somewhere else around here.
17:34 ... 50 × 8 = 400; 9 × 4 = 27; 400 - 27 = 373; 373 - 8 = 365; 365 + 3 = 368
21:42 ... was doable, according to the webpage I found that has a solver; I know when I'm out of my league. Our courteous host Björn left that bit out... or else the show had to cut it for time.
25:26 ... 8 - 2 = 6; 6 × 6 =36; 36 × 10 = 360; 5 × 5 = 25; 360 - 25 = 335
I did get the 512, but it was the same as the players.
You can assume that I missed all the rest.
Actually, Rachel solved the target 663 as 39 x 17 (the same method as most of us) in Wednesday after the Conundrum.
Must have fast forwarded over that when I was editing the video. I did catch her post-conundrum-solve on the Friday episode though.
638 was easy, i used the same manner but for found it quicker than here, always have been good at calculating
4:43 Rachel deliberately chooses the most difficult solution in order not to embarrass the candidates.
(6/2)+10 also gets you 13. It was quite hard not to see that.
My thoughts exactly. Riley should think of us numpties at home, we want the simple stuff.
@@mm9773 That's not the point I was trying to make.
@@jacquesmertens3369 No, I know - but it’s the point I am making. But I also think the simpler solution is more elegant.
33:16 Holy crap I just found one that Rachel couldn't do that I did in like 5 seconds!!!!! (9+8)*25*2 = 850 - (5/5) = 849
382 is 8-1 = 7 * 9 * 6 = 378 + 4 = 382
I got 322 but I forgot the way I got is
980 75-5=70 25-8-3=14×70=980
Rachel's 13 at 4:56 is as complicated as it could be xD i just did 10 + 6/2
Or just 10*25 + 8*8 + 6/2
638 9×50=450 8×25=200 9+3=12 =450+200-12=638
Tuesday:
186:
25 * 7 = 175
175 + 6 + 5 = 186
25 * 6 = 150
8 * 5 = 40
150 + 40 - 7 + 3 = 186
From factoring:
25 + 6 = 31
5 + 8 - 7 = 6
31 * 6 = 186
and
6 * 5 = 30
25 + 30 + 7 = 62
62 * 3 = 186
and
25 - 7 = 18
18 * 5 = 90
90 + 3 = 93
8 - 6 = 2
93 * 2 = 186
638:
50 + 8 = 58
9 * 3 = 27
27 - 25 + 9 = 11
58 * 11 = 638
909:
6 * 75 = 450
450 + 5 = 455
455 * 2 = 910
10 / 10 = 1
910 - 1 = 909
980:
75 - 5 = 70
25 - 8 - 3 = 14
70 * 14 = 980
8 * 5 = 40
75 + 25 + 40 = 140
4 + 3 = 7
140 * 7 = 980
25 * 8 = 200
200 - 4 = 196
196 * 5 = 980
4 * 3 = 12
25 - 12 = 13
75 * 13 = 975
975 + 5 = 980
10+2=12×75=900 6-5=1 10-1=9 900+9
368 75-3=72÷9=8 50-3=47×=376-8=368
335=5×(6×10+5+2)
(50 + 8 - 3) × 6 × 2 = 660
Monday:
322:
100 + 6 = 106
106 * 3 = 318
318 + 4 = 322
100 + 10 = 110
110 * 3 = 330
330 - 10 + 6 - 4 = 322
100 - 10 - 10 = 80
80 * 4 = 320
6 / 3 = 2
320 + 2 = 322
10 * 4 = 40
40 + 6 = 46
10 - 3 = 7
46 * 7 = 322
100 - 4 = 96
96 * 10 = 960
960 + 6 = 966
966 / 3 = 322
141:
Several possible solutions, but I spotted only one solution by factoring (141 = 3 * 47)
9 * 8 = 72
72 - 25 = 47
8 / 4 = 2
6 / 2 = 3
47 * 3 = 141
317:
25 * 10 = 250
8 * 8 = 64
6 / 2 = 3
250 + 64 + 3 = 317
10 * 8 * 8 = 640
640 - 6 = 634
634 / 2 = 317
There was also a solution similar to Rachel's, but with a much easier way to reach 13:
6 / 2 = 3
10 + 3 = 13
25 * 13 = 325
325 - 8 = 317
960:
100 + 50 + 9 + 1 = 160
160 * 6 = 960
50 - 1 - 9 = 40
40 * 4 * 6 = 960
322 4×10=40+6=46 10-3=7=46=322
50+6=56+3=59+7=66 8+2=10 66×10=660
186 7×25=175+8+3=186
141 6×25=150-9
660 = 50+8-3 55 & 2*6 = 12 & 55*12 = 660
849 I beat Rachel AND Colin with Rachel's eventual solution
186 without the 25
.
.
.
.
.
(8*3+7)*6
Since 512 = 2^9
.
.
.
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8*8*4*(7-6+1)
660 50+8-3=55 2×6=12×55=660
the 849 is easy though: 9+8 = 17 & 25*2 = 50 so 50*17 = 850 & 5/5 = 1 so 850-1 = 849
Oh she did found that quite easy solution though it took her long
50+25-3=72 *9 = 638
141
25×6=150-9=141
909 10+2=12×75=900 +10-6+5=909
317 6÷2=3+10=13×25=325-8=317
[9 × (8 - 1) × 6] + 4 = 382
In the first round of Monday, I saw both contestants' solutions, but one can use factoring (23 x 7 x 2 = 322) to solve it as a "five small":
10 x 4 = 40
40 + 6 = 46
10 - 3 = 7
46 x 7 = 322
And I also had this similar solution to Rick:
100 + 6 = 106
106 x 3 = 318
318 + 4 = 322
Finally, I had this solution:
100 - 10 - 10 = 80
80 x 4 = 320
6 / 3 = 2
320 + 2 = 322
In the second round, I saw Rick's solution, but also had these solutions:
25 + 8 = 33
33 x 4 = 132
132 + 9 = 141
9 + 6 = 15
15 x 8 = 120
120 + 25 = 145
145 - 4 = 141
8 + 4 = 12
12 x 9 = 108
108 + 25 = 133
133 + 8 = 141
In the third round, I got Rachel's solution, except she did it in a complex way to hide how easy it was. She could have done the following:
6 / 2 = 3
10 + 3 = 13
25 x 13 = 325
325 - 8 = 317
Another thing she could have done was this:
25 x 10 = 250
8 x 8 = 64
250 + 64 = 314
6 / 2 = 3
314 + 3 = 317
Finally, you can solve it as a "five small" in this way:
10 x 8 x 8 = 640
640 - 6 = 634
634 / 2 = 317
In the final round, I saw both contestants' solution, but I was surprised they didn't go for other easy solutions, like the following:
100 - 4 = 96
9 + 1 = 10
96 x 10 = 960
100 + 50 + 9 + 1 = 160
160 x 6 = 960
50 - 9 - 1 = 40
40 x 6 x 4 = 960
I'll post my solutions for Tuesday's game in another comment below this.
In the first round of Tuesday, I had these "five small" solutions from factoring (31 x 3 x 2 = 186):
8 x 3 = 24
24 + 7 = 31
31 x 6 = 186
8 x 7 = 56
56 + 6 = 62
62 x 3 = 186
And these easy solutions with the 25:
25 x 7 = 175
175 + 6 + 5 = 186
8 - 7 = 1
25 + 5 + 1 = 31
31 x 6 = 186
25 - 7 = 18
8 + 5 = 13
13 - 3 = 10
18 x 10 = 180
180 + 6 = 186
In the second round, I saw Rachel's solution, but I also had this one based on factoring (29 x 11 x 2 = 638):
50 + 8 = 58
9 x 3 = 27
27 + 9 = 36
36 - 25 = 11
58 x 11 = 638
I couldn't see any other solutions, though.
In the third round,. I saw Rick's solution and this other one:
75 x 6 = 450
450 + 5 = 455
455 x 2 = 910
10 / 10 = 1
910 - 1 = 909
Again it's the only other one I could spot, so either I'm having a moment of mental dullness here or these are some seriously difficult problems.
In the final round, I saw Rachel's solution. However, Rick was very nearly there with his solution. He should have done this:
4 x 3 = 12
25 - 12 = 13
75 x 13 = 975
975 + 5 = 980
Another easy way is:
25 x 8 = 200
200 - 4 = 196
196 x 5 = 980
Finally, I also had this:
75 - 5 = 70
25 - 8 - 3 = 14
70 x 14 = 980
In the first round on Wednesday, I saw Rick's solution but also factored (11 x 5 x 3 x 2^2 = 660) for these solutions:
50 x 2 = 100
100 + 7 + 3 = 110
110 x 6 = 660
8 - 3 = 5
50 + 5 = 55
55 x 6 x 2 = 660
50 - 6 = 44
8 + 7 = 15
44 x 15 = 660
In the second round, I saw Rachel's solution, and also had these (the first one was so easy to spot I saw it before the clock started):
50 x 9 = 450
450 - 75 - 8 = 367
3 / 3 = 1
367 + 1 = 368
50 - 3 = 47
75 - 3 = 72
72 / 9 = 8
47 x 8 = 376
376 - 8 = 368
75 + 50 = 125
125 x 9 = 1125
1125 + 3 = 1128
1128 / 3 = 376
376 - 8 = 368
In the third numbers round, I saw Rick's solution and also had these:
25 x 6 x 3 = 450
8 / 4 = 2
7 x 2 = 14
450 - 14 = 436
8 - 7 = 1
25 - 1 = 24
24 x 6 x 3 = 432
432 + 4 = 436
And this one from factoring (109 x 2^2 = 436):
25 - 8 = 17
17 x 6 = 102
102 + 7 = 109
109 x 4 = 436
In the fourth round, I had the unusual pleasure of beating Rachel in a numbers round and doing it in the 30 seconds. The following is the only way I have seen, however, so it's no reflection on her that she didn't get it:
75 + 3 = 78
78 x 50 = 3900
25 - 8 = 17
3900 x 17 = 66300
66300 / 100 = 663
Admittedly, you can do 100 / 50 = 2 and divide by 2, so you don't need to go into the tens of thousands, but when you have a four-large game why not have some fun with it? I got this by factoring (17 x 13 x 3 = 663). 78 is twice 39, so if you add 3 to 75, then divide it by 2 (or break it up as I did), then you'll get 39 x 17 = 663.
In the first round on Thursday, I saw Peter's solution, and also had these solutions by factoring (13 x 5 x 2^2 = 260):
5 x 2 = 10
75 - 10 = 65
3 + 1 = 4
65 x 4 = 260
75 / 3 = 25
25 + 1 = 26
26 x 5 x 2 = 260
8 x 3 = 24
75 - 24 = 51
51 + 1 = 52
52 x 5 = 260
8 + 3 = 11
11 x 2 = 22
75 - 22 = 53
53 - 1 = 52
52 x 5 = 260
In the second round, I saw Peter's method of getting 67 and also had this one:
10 + 2 = 12
12 x 6 = 72
72 - 5 = 67
67 x 5 = 335
And I had these related solutions:
8 x 5 = 40
40 - 6 = 34
34 x 10 = 340
340 - 5 = 335
6 x 5 = 30
8 / 2 = 4
30 + 4 = 34
34 x 10 = 340
340 - 5 = 335
In the third numbers round, I saw both contestants' solutions and also had these solutions:
100 / 4 = 25
25 x 7 = 175
175 + 8 = 183
183 x 4 = 732
100 - 8 = 92
9 - 7 = 2
92 x 4 x 2 = 736
736 - 4 = 732
In the final numbers round, I saw Colin's solution, and also had these ones:
10 - 4 = 6
9 x 7 x 6 = 378
378 + 1 = 379
10 x 9 = 90
90 + 1 = 91
91 x 4 = 364
364 + 8 + 7 = 379
I'll come back and finish Friday later.
In the first numbers round on Friday, I saw Peter's solution, of course. It's so good that I'm almost tempted to just leave it, but in the interests of having something else to say I also came up with these alternatives:
8 + 4 = 12
12 x 6 = 72
72 - 7 - 1 = 64
64 x 8 = 512
7 + 6 + 1 = 14
14 x 4 = 56
56 + 8 = 64
64 x 8 = 512
8 + 4 = 12
12 x 7 x 6 = 504
504 + 8 = 512
In the second round, I'm surprised it took Rachel so long to come up with the solution. I saw hers in the 30 seconds, as well as this one:
8 x 5 = 40
40 + 2 = 42
25 - 5 = 20
42 x 20 = 840
840 + 9 = 849
In the third round, with the 8 on the board it was odd neither Rachel nor the contestants tried to come at the target via 390, which can be done in the following way:
9 + 4 = 13
13 x 6 x 5 = 390
390 - 8 = 382
And I also had these two related solutions:
8 - 1 = 7
9 x 7 x 6 = 378
378 + 4 = 382
8 x 6 = 48
48 - 5 - 1 = 42
42 x 9 = 378
378 + 4 = 382
In the final numbers round, I beat Rachel to the solution again, getting my solutions well within the 30 seconds, but I was helped by working out the factors of 638 (29 x 11 x 2 = 638) only yesterday, because this was the target of the second numbers round on Tuesday's show. My solutions based on factoring are:
25 - 6 = 19
19 x 3 = 57
57 + 1 = 58
8 + 3 = 11
58 x 11 = 638
6 + 1 = 7
7 x 3 = 21
21 + 8 = 29
25 - 3 = 22
29 x 22 = 638
8 x 3 = 24
6 - 1 = 5
24 + 5 = 29
25 - 3 = 22
29 x 22 = 638
Sorry the 186 was so easy that their way cinfused ne.
Just das 25*7= 175+6+5
960 100+50+9+1=160×6=960
909
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75*(10+2)+(10+5-6)
{25 × [10 + (6 / 2)]} - 8 = 317
She is extremely well with numbers but so am i, not going to say i have anything on her but she certainly not on me either
Wednesday:
660:
8 - 3 = 5
50 + 5 = 55
55 * 2 * 6 = 660
50 * 2 = 100
100 + 7 + 3 = 110
110 * 6 = 660
6 / 2 = 3
50 + 7 + 3 = 60
8 + 3 = 11
60 * 11 = 660
50 - 6 = 44
8 + 7 = 15
44 * 15 = 660
368:
50 * 9 = 450
3 / 3 = 1
8 - 1 = 7
450 - 75 - 7 = 368
9 + 3 = 12
12 / 3 = 4
50 - 4 = 46
46 * 8 = 368
436:
25 - 8 = 17
17 * 6 = 102
102 + 7 = 109
109 * 4 = 436
7 * 6 * 3 = 126
126 - 25 + 8 = 109
109 * 4 = 436
663:
I found a solution by factoring:
75 + 3 = 78
100 / 50 = 2
78 / 2 = 39
25 - 8 = 17
39 * 17 = 663
For Monday:
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In the first round, the contestants' solutions are obvious. Apart from the solutions, there are several ways to obtain the target:
100 + 6 = 106
3 x 106 = 318
318 + 4 = 322
100 + 10 = 110
3 x 110 = 330
10 + 4 = 14
14 - 6 = 8
330 - 8 = 322
4 x 10 = 40
40 - 3 = 37
37 x 6 = 222
222 + 100 = 322
100 - 10 - 10 = 80
80 x 4 = 320
6 / 3 = 2
320 + 2 = 322
Besides, it is noticed that 322 = 2 x 7 x 23, so it is possible to obtain the target with the small numbers:
4 x 10 = 40
40 + 6 = 46
10 - 3 = 7
46 x 7 = 322
The second round is another easy round. Rick's solution is immediately obtained before the clock started. In addition, there are some alternate solutions found:
25 - 6 = 19
19 x 8 = 152
8 / 4 = 2
9 + 2 = 11
152 - 11 = 141
25 - 8 = 17
17 x 8 = 136
9 - 4 = 5
136 + 5 = 141
25 + 8 = 33
33 x 4 = 132
132 + 9 = 141
Since 141 = 3 x 47, one way to obtain the target with factoring is:
9 x 8 = 72
72 - 25 = 47
6 x 4 = 24
24 / 8 = 3
47 x 3 = 141
For the third round, it is a bit tricky because all small numbers are even. While there are many ways to get one-away (either 316 or 318), a simpler way to Rachel's solution is:
6 / 2 = 3
10 + 3 = 13
13 x 25 = 325
325 - 8 = 317
It seems that the only way to obtain the target is making 325.
For the last round, the contestants' solution can be obtained without any effort. Apart from that, there are a couple of ways to obtain the target using factoring:
100 + 50 + 9 + 1 = 160
160 x 6 = 960
50 - 9 - 1 = 40
40 x 4 x 6 = 960
Besides, there are several other intuitive ways:
9 + 1 = 10
10 x 100 = 1000
1000 - 50 = 950
950 + 4 + 6 = 960
100 - 4 = 96
9 + 1 = 10
96 x 10 = 960
For the other days, I will post in separate comments.
For Tuesday:
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The first round is easy and there are lots of ways to obtain the target. I was expecting the contestants could get this one:
25 x 7 = 175
6 + 5 = 11 (or 8 + 3 = 11)
175 + 11 = 186
Apart from Rulus's solution, there are several ways to obtain the target based on factoring (186 = 31 x 2 x 3):
25 + 6 = 31
5 + 8 - 7 = 6
31 x 6 = 186
25 + 6 = 31
7 - 5 = 2
31 x 2 x 3 = 186
8 x 7 = 56
56 + 6 = 62
62 x 3 = 186
3 x 8 = 24
24 + 7 = 31
31 x 6 = 186
Besides, there are several other alternatives, with the first one similar to Rulus's solution:
25 x 8 = 200
5 - 3 = 2
2 x 7 = 14
200 - 14 = 186
25 + 5 - 7 = 23
23 x 8 = 184
6 / 3 = 2
184 + 2 = 186
For the second round, since 638 = 2 x 11 x 29, there is one way to obtain the target with factoring:
50 + 8 = 58
9 x 3 = 27
9 + 27 = 36
36 - 25 = 11
11 x 58 = 638
For the third round, I get Rick's straight-forward solution, but I cannot find any alternative for this one.
For the fourth round, it is noticed that 980 = 2 x 2 x 5 x 7 x 7, in addition to Rachel's solution, there are several ways to obtain the target with factoring:
75 - 5 = 70
25 - 8 - 3 = 14
14 x 70 = 980
25 x 8 = 200
200 - 4 = 196
196 x 5 = 980
25 + 3 = 28
8 x 5 = 40
75 - 40 = 35
28 x 35 = 980
For Wednesday:
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For the first round, there are lots of ways to obtain the target. Apart from Rick's obvious solution, I got several alternatives using factoring:
50 x 2 = 100
100 + 7 + 3 = 110
110 x 6 = 660
50 + 3 - 8 = 55
55 x 6 x 2 = 660
8 x 2 = 16
50 + 16 = 66
7 + 3 = 10
66 x 10 = 660
For the second round, I also noticed that 368 = 46 x 8, so I got Rachel's solution within the 30 seconds. Apart from Rachel's solution, I got one alternative:
50 x 9 = 450
3 / 3 = 1
450 + 1 = 451
451 - 75 - 8 = 368
The third round is another easy round. It is easy to notice that 436 = 109 x 4, which means one way to obtain the target is to make 109, and it is doable as:
7 x 6 = 42
42 - 8 = 34
25 x 3 = 75
34 + 75 = 109
109 x 4 = 436
Besides, it is possible to achieve the target from 450 as:
25 x 6 x 3 = 450
8 / 4 = 2
7 x 2 = 14
450 - 14 = 436
For the fourth round, I got the solution using factoring, as 663 = 13 x 3 x 17:
25 - 8 = 17
75 + 3 = 78
100 / 50 = 2
78 / 2 = 39
17 x 39 = 663
For Thursday:
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The first round is an easy round. I get Rick's solution in almost a second. Apart from the contestants' solutions, I get several alternatives using factoring:
8 + 2 = 10 (or 5 x 2 = 10)
75 - 10 = 65
3 + 1 = 4 (or 5 - 1 = 4)
65 x 4 = 260
75 / 3 = 25
25 + 1 = 26
26 x 5 x 2 = 260
3 x 8 = 24
75 - 24 + 1 = 52
52 x 5 = 260
For the second round, it is easily spotted that 335 = 67 x 5, so I got the same solution as Peter's. Besides, I found similar alternatives:
2 + 8 = 10
6 x 10 = 60
60 + 5 = 65
65 x 5 = 325
325 + 10 = 335
6 x 10 = 60
60 + 8 - 2 = 66
66 x 5 = 330
330 + 5 = 335
The third round is another easy round. I got Peter's solution after Rachel saying the target. Apart from the contestants' solutions, I get one alternative using factoring:
9 x 8 = 72
72 + 7 + 4 + 100 = 183
183 x 4 = 732
For the fourth round, apart from Colin's easy solution, I obtain an alternative instead:
10 + 4 = 14
14 - 8 = 6
6 x 7 x 9 = 378
378 + 1 = 379
For Friday:
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For the first round, since 512 = 2^9 is a 101 fact in computer science, so I got an alternative solution immediately:
7 - 6 + 1 = 2
2 x 4 x 8 x 8 = 512
For the second round, I got Rachel's solution in a few seconds, since it is easily spotted that 850 = 34 x 25. However, I cannot find any alternative for this one.
For the third round, since I like to make number divisible by 3 and 9, so apart from Rachel's solution, I found another way to achieve the goal, based on the solution I found for 379 from previous day:
8 - 1 = 7
6 x 7 x 9 = 378
378 + 4 = 382
For the final round, I found Rachel's solution after a few tries. Besides, I found that 638 = 2 x 11 x 29. Therefore, a couple of alternatives by factoring are:
6 + 1 = 7
3 x 7 = 21
21 + 8 = 29
25 - 3 = 22
29 x 22 = 638
3 x 8 = 24
24 + 6 - 1 = 29
25 - 3 = 22
29 x 22 = 638
25 - 6 = 19
19 x 3 = 57
57 + 1 = 58
8 + 3 = 11
58 x 11 = 638
638 using 58*11
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(50+8)*(9*3 - 25 + 9)
Another way to get 980. 75 x 3 = 225 + 25 = 250 - 5 = 245 x 4 = 980.
The easier way to get 368 is: 50 - 3 = 47 x 8 = 368.
436 in another unusual.
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(25*3 + 7*6 - 8)*4
(75 - 5) × (25 - 8 - 3) = 980
[(10 - 4) × 9 × 7] + 1 = 379
660.
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(50*2+7+3)*6