# Number Factoring Game

This is an old math exercise often called the "Taxman". Here's how it works.

Pick a number from the board

You get the value of the number

Your opponent, the taxman, gets all the factors of that number that remain on the board

When no more numbers remain that have factors, the taxman gets all those too!

Congratulations!

You beat the taxman by .

You beat the taxman by .

You lost by

ðŸ˜ž

You tied the taxman

Score:

0-0

Your Picks:

Taxman's Take:

Quizmaster

After many tries, I beat the taxman by 303. I could write a computer program to find the perfect answer, but that would ruin the fun! Is it possible to beat the taxman by more than 303?

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Jun 14, 2016

kiwirage

(57)

Fun! Yes, there's a way to beat him by 325 :)

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Jun 14, 2016

Quizmaster

Impressive! I can't figure out how to do it.

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Jun 15, 2016

Quizmaster

Another challenge is to see how much you can lose by. The most I am able to lose by is 541, but I think it's possible to do worse.

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Jun 15, 2016

Quizzer6794

(57)

2, 8, 6, 28, 25, 22, 20, 26, 18, 32, 24, 34, 38, 42, 46, 45 = -443 (worst)

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Jun 15, 2016

Arp2600

(69)

It's possible to lose by 633 points.

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Jun 15, 2016

Symmetrik

(60)

I managed to lose by 549, my biggest loss so far.

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Jun 16, 2016

Arp2600

(69)

I found a 808-467 solution, so a difference of 341. Still not quite sure it's the best possible.

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Jun 15, 2016

Arp2600

(69)

After some research, I am now convinced that 808-467 (+341) is the best win and that 296-979 (-683) is the worst loss.

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Jun 16, 2016

Deddryk

(61)

Wow! I managed 800-475 for a 325 point win by always picking the largest number with only one factor left. How did you push it up to 808-467?

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Jun 16, 2016

Arp2600

(69)

I don't know how you did it, but I would say... try taking 28 instead of 20.

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Jun 16, 2016

Deddryk

(61)

Actually I see where my algorithm fails to be optimal. Near the end it basically trades 32 for 24 unnecessarily. I wonder if anyone has proven an optimal algorithm for this game.

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Jun 16, 2016

Arp2600

(69)

Maybe you take out 48 too early ?

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Jun 16, 2016

Deddryk

(61)

No, the last three strictly following my algorithm are 24, 48, 40, which is not as good as instead picking 32, 48, 40 which gets my score to match yours.

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Jun 16, 2016

Arp2600

(69)

So did you do it? I think you can just take 32 instead of 24...

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Jun 16, 2016

Deddryk

(61)

Yeah I did. I'm just curious as to whether or not there is an algorithm that will always give you the correct result (ie if the quiz went to 75 instead of 50).

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Jun 16, 2016

SouthwestChief

(44)

Deddrk, I used your algorithm and only won by 149 points.

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Jun 19, 2016

Quizmaster

I used @Deddryk's algorithm and lost by 253.

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Jun 20, 2016

Alex99

(37)

Yep, I agree. got 808-467, quite challenging, nice job in finding highest and lowest.

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Oct 21, 2016

Quizzer6794

(57)

To relate back to the JetPunk quiz area, could this perhaps earn you points, dspending on how many points you won by? Very cool game.

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Jun 14, 2016

Gamer1162

(55)

By randomly choosing numbers, I only lost by 99, my closest

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Jun 15, 2016

bluesdjben

(63)

I tried it about a dozen times before winning by 61.

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Jun 15, 2016

Nuna

(1)

YES I beat him by 103 points, my trick was to start out by avoiding any numbers that are divisible by 2,3, and 4, which mostly left numbers only divisible by 5, and 7 then gradually started with numbers that were divisble by 3 then finally the ones with 2. But you always have to make sure the number you choose is the largest possible, always compare with the numbers in the diagonal row with that number. it took about 10 mins for my game so be patient

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Jun 15, 2016

roddyrockstar

(60)

I did your way, and managed to beat taxman by 1

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Jun 20, 2016

Symmetrik

(60)

Took a few tries, but it was my 4th or 5th I finally won, by 49.

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Jun 15, 2016

Symmetrik

(60)

Wow. That was close. Beat him by 1, 638-637. Makes it even sweeter.

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Jun 15, 2016

Sulps

(56)

2nd try. I beat the taxman by 87 points. It was surprisingly mind-challenging.

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Jun 15, 2016

swag11

(34)

HOW DO YOU DO IT!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1

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Jun 15, 2016

yusra

(46)

Love this game!!

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Jun 15, 2016

Sakurai

(47)

After few times, I won by 21 points ;)
648-627

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Jun 15, 2016

Seattle419

(59)

first try 638-637 dub. Phew!

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Jun 15, 2016

Arp2600

(69)

That's another challenge indeed. How to make the closest win and the closest loss.

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Jun 16, 2016

Arp2600

(69)

Ah ha, found both 637-638 and 638-637. It's a bit less logical than the extreme cases, but still fun.

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Jun 16, 2016

cosmokim

(54)

2 tries, beat him by 43

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Jun 15, 2016

odalley1

(43)

I know the first number should be the highest prime number as you pretty much have to lose all the prime numbers... Took me about 5 goes to win by 25

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Jun 15, 2016

billz

(60)

47, 49 is a solid start

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Jun 15, 2016

Quizzer6794

(57)

After 3 tries I got him by 125. Hard but fun!

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Jun 15, 2016

eurocrem

(45)

After a few tries, i won by 3 :D

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Jun 15, 2016

eurocrem

(45)

11

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Jun 15, 2016

hi

(42)

After many unsuccessful tries, I finally beat the taxman by 25!!!!!!!!

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Jun 15, 2016

hi

(42)

Now 195!!!

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Jun 16, 2016

jayjay068

(25)

You can't win :(

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Jun 15, 2016

Gandalf9010

(44)

Finally beat him, but only by 45. I'm gonna keep trying.

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Jun 15, 2016

Gamer1162

(55)

I beat him by 7, I feel satisfied

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Jun 15, 2016

Instrumental

(48)

Beat him by 21 points in three tries. It was easy to win, but I'm more interested in figuring out the algorithm to beat him consistently instead of winging it on what seemed like a good choice. Obviously that was good enough to work, but it isn't the true answer to this problem.

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Jun 15, 2016

sf49ers

(77)

It seems that there is one important piece of information missing from the directions--that when a number has no more factors (regardless of whether you have selected it or a number it is a factor of) it becomes unavailable to pick. I could not figure out why when I selected 36, 24 was eliminated...

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Jun 16, 2016

jmellor13

(52)

For the math challenged (like me): I would start with high numbers with very few factors. Start with 47, the highest prime. Next, take 49 because it's only factor is 7, so after those two moves, you're winning 96-8. Then grab the numbers whose only factors are prime numbers that are already off the board. After the first selection, all the primes come off the board because their only factor is 1. So take 38, because you've already lost 19. Take 46 because you've already lost 23. Take 34 because you've already lost 17. Next, be careful about the multiples of 4 and 8. It's tempting to take 48, but then you lose 4, 6, 8, 12, 16, 24, and then, because all its factors are gone, 32. That's a bad trade. Wait until only one or two of those factors are left to grab 48. Instead, think from the middle. Take 22 before 44, because the factor 4 will keep 44 alive, but if you take 44 first, you'll lose 22. I'm sure there is a more exact science, but this has been working for me.

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Jun 16, 2016

Arp2600

(69)

47-49 is the obvious beginning. After that, what you say is a winning strategy, but the best is a bit subtler.

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Jun 16, 2016

Quizzer6794

(57)

There would be no point picking 48 and 36 because the taxman can still take those numbers anyway

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Jun 16, 2016

Liverpool03

(54)

Just lost by 1 by basically guessing the whole thing ;~;

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Jun 19, 2016

geographyisthebestsubject

(21)

Very creative and fun quiz!

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Jun 20, 2016

Arp2600

(69)

Ok, a few days have passed, so let's explain how to make the maximum. So : SPOILER ALERT. If you don't want to know, don't read...

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Jun 20, 2016

Arp2600

(69)

As already said above, there are a few rules to follow, basically to take only numbers with one divisor left. The first number will always take the divisor 1, so you have to begin with a prime number, logically the largest available : 47. After that, all of the other prime numbers become grey, which means you can't take them. It's not a problem for those inferior to 25, you can use them to grab their doubles later. But 29, 31, 37, 41, 43 will remain on the board and will be taken by the taxman in the end.

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Jun 20, 2016

Arp2600

(69)

Those 5 numbers are lost, thus only 45 can be used, which makes a maximum of 22 pairs, plus a wasted number. Either the taxman takes a sixth number in the end or you pair a number with two divisors instead of one at some point, but 22 is definitely the maximum number of numbers you can take during the game. This sets an upper bound to the score : the sum of the 22 biggest numbers is 818.

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Jun 20, 2016

Arp2600

(69)

So you have to try to take most of the biggest numbers, which requires a bit of thinking and a good ordering. Deddryk's method is almost perfect, because it's what you want to do : pick the highest numbers with only one divisor left... So, after 47, you must take the biggest square of a prime number, namely 49. After that you have to take the highest multiple of 7 and another prime number : 35.

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Jun 20, 2016

Arp2600

(69)

The next step is a little bit trickier... the fact is that, at this stage, all numbers greater than 21 have at least two divisors left. You would want to remove something larger than that but you can't really do that. 21 is the best choice, better than 15 anyway (both 21 and 15 remove only the divisor 3, but... 21 is bigger). After 21, things become more open... 27, 33 and 39 remove only 9, 11 and 13 respectively, and when 9 is gone, you can also take 45.

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Jun 20, 2016

Arp2600

(69)

After that, it's time to remove 2. The best number to do that is 26, since 13 is already taken, (and you will need 22 to remove 44). Then you can take all of the remaining doubles of prime numbers left : 46, 38 and 34. So, if we recapitulate, we have removed 12 big numbers : 47-49-35-21-39-33-27-45-26-46-38-34.

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Jun 20, 2016

Arp2600

(69)

Then, the most frustrating step... at this stage, most numbers have two or more divisors left, so you have to take a rather low number... the best thing to do is to remove 18 with the divisor 6. Back to the big ones next : 42 with 14, 28 with 4, 30 with 10, 44 with 22, 50 with 25, 36 with 12.

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Jun 20, 2016

Arp2600

(69)

Apart from the high primes, there are 7 numbers left on the board, that can be paired to make the best score : 8, 16, 20, 24, 32, 40, 48. You can either take 32 or 40, then the other, they will remove the divisors 8, 16 and 20. And finally you reach the score 808 by taking 48 with 24. Up to a few possible permutations, the solution is : 47-49-35-21-39-33-27-45-26-46-38-34-18-42-30-28-50-44-36-40-32-48

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Jun 20, 2016

joeythelemur

(70)

Third try, won by 145! Fun game!

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Jul 18, 2016

Jen81

(33)

I won by 33 on my first attempt, without really understanding what I was doing! Beginner's luck. Having read the comments I now have a clearer idea, so will try again...and probably lose drastically!

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Jul 22, 2016

Jen81

(33)

Yup, lost by 199!

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Jul 22, 2016

BAMALAMIAN

(34)

47, 49, 25, 39, 26, 8, 50, 45, 40, 46, 38, 34, 12, 22, 28, 32, 36, 42, 48...667-608 win

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Aug 15, 2016

wtstoudt

(58)

But can you tie?

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Aug 16, 2016

JBlouw1850

(43)

Nope. Add all the numbers together and you get an odd number.

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Oct 31, 2016

ChaosQuizzer

(22)

47, 49, 35, 21, 39, 33, 27, 45, 26, 46, 38, 34, 18, 42, 30, 50, 28, 44, 40, 36, 32, 48 - 808-467. I thought I messed it up when I clicked the 40 when it had 2 factors out (8 and 20). Win by 341.

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Aug 24, 2016

Azerk

(16)

aww

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Aug 25, 2016

ANIMEG123

(16)

I DID WITH 341 POINTS

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Sep 27, 2016

GeneraliGeeks

(47)

Eh?

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Oct 5, 2016

SuperSans321

(6)

After a few fails, I finally beat the taxman by 17: 646-629. I used billzs
protip and started with 47, 49.

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Oct 6, 2016

Matthew07

(34)

Finally won 693-582

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Oct 12, 2016

MyMindWentBlank

(39)

Is your score the sum of your selections?

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Oct 15, 2016

KoljiVriVoda

(62)

641-634. I don't know how... For now.

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Oct 17, 2016

nmaec

(29)

Bet him on the 3rd try by 23

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Oct 20, 2016

Alex99

(37)

For those who are suffering, here is the solution. If i get complaints that I am giving it to them, I will delete my post. Quizmaster can remove it anytime if he feels like it, I don't mind.
This is how to get 808-467 (+341)
47 49 35 21 39 33 27 45 26 46 38 34 18 42 30 28 44 40 36 32 48

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Oct 21, 2016

Alex99

(37)

So far for me biggest win is 341 and biggest loss is 633, not quite optimal :(

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Oct 21, 2016

TheNerdKid351

(37)

Is this even possible? Best score: lose by 65

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Oct 29, 2016

karkatfan12

(4)

OMG i won
(by 43)

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Nov 1, 2016

3275

(25)

win 498
loss 684

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Nov 26, 2016

Rougecompany

(42)

I lost by just 17... So close

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Dec 12, 2016

Soccerstud

(31)

Beat it by 647

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Dec 15, 2016

eversj

(15)

Beat it by 647

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Dec 15, 2016

danny11mcl

(20)

beat it by 647 also

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Dec 15, 2016

BlorbyFuncho83

(36)

I beat him by 15 by randomly guessing numbers. WOW

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Dec 16, 2016

BlorbyFuncho83

(36)

My picks (Backwards): 23 28 92 72 83 81 54 44 94 82 43 93 63 24 64 04 05 84

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Dec 16, 2016

yobhdgmu

(30)

lost by 83

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Dec 17, 2016

Tomasquilmes

(3)

I won by 1 (638-637)

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Dec 27, 2016

DrDragon

(20)

Beat him by 75

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Jan 5, 2017

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