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

π

You tied the taxman

Score:

0-0

Your Picks:

Taxman's Take:

Quizmaster

+1

level β

Jun 14, 2016

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?

kiwirage

+1

level 61

Jun 14, 2016

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

Quizmaster

+1

level β

Jun 15, 2016

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

Quizmaster

+1

level β

Jun 15, 2016

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.

Quizzer6794

+1

level 58

Jun 15, 2016

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

Arp2600

+1

level 74

Jun 15, 2016

It's possible to lose by 633 points.

Symmetrik

+1

level 59

Jun 16, 2016

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

QuizBeater101

+1

level 7

Mar 4, 2017

I lost by 435 (420-855) by picking 2, 48, 10, 14, 18, 22, 26, 30, 34, 38, 40, 42, 46, 50

atomicbomb1213124124

+1

level 17

Sep 14, 2017

I managed to lose by 683 with 23, 25, 15, 21, 14, 22, 20, 16, 18, 24, 26, 38, 34

Arp2600

+1

level 74

Jun 15, 2016

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

Arp2600

+1

level 74

Jun 16, 2016

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

Deddryk

+1

level 62

Jun 16, 2016

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?

Arp2600

+1

level 74

Jun 16, 2016

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

Deddryk

+1

level 62

Jun 16, 2016

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.

Arp2600

+1

level 74

Jun 16, 2016

Maybe you take out 48 too early ?

Deddryk

+1

level 62

Jun 16, 2016

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.

Arp2600

+1

level 74

Jun 16, 2016

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

Deddryk

+1

level 62

Jun 16, 2016

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).

SouthwestChief

+1

level 49

Jun 19, 2016

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

Quizmaster

+1

level β

Jun 20, 2016

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

Alex99

+1

level 37

Oct 21, 2016

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

catlover2496

+1

level 40

Feb 3, 2017

There's a way to beat him by 17! 646-629

WolfCam

+1

level 57

Mar 16, 2018

I won by 3... I started with doing 47, 49,21,27,33,39,45, then all the even numbers in decreasing order starting at 48. Then lastly, 50.

Quizzer6794

+2

level 58

Jun 14, 2016

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.

Gamer1162

+1

level 64

Jun 15, 2016

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

DACOW

+1

level 36

Jun 24, 2017

lol, thats my best score actually trying

bluesdjben

+1

level 67

Jun 15, 2016

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

Nuna

+1

level 1

Jun 15, 2016

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

roddyrockstar

+1

level 61

Jun 20, 2016

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

Symmetrik

+1

level 59

Jun 15, 2016

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

Symmetrik

+1

level 59

Jun 15, 2016

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

Sulps

+1

level 61

Jun 15, 2016

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

swag11

+1

level 34

Jun 15, 2016

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

yusra

+1

level 48

Jun 15, 2016

Love this game!!

Sakurai

+1

level 47

Jun 15, 2016

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

Seattle419

+1

level 59

Jun 15, 2016

first try 638-637 dub. Phew!

Arp2600

+1

level 74

Jun 16, 2016

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

Arp2600

+1

level 74

Jun 16, 2016

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

cosmokim

+1

level 55

Jun 15, 2016

2 tries, beat him by 43

odalley1

+1

level 47

Jun 15, 2016

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

billz

+1

level 60

Jun 15, 2016

47, 49 is a solid start

Quizzer6794

+1

level 58

Jun 15, 2016

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

eurocrem

+1

level 45

Jun 15, 2016

After a few tries, i won by 3 :D

eurocrem

+1

level 45

Jun 15, 2016

11

Saharan

+1

level 32

Jan 9, 2018

67

hi

+1

level 42

Jun 15, 2016

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

hi

+1

level 42

Jun 16, 2016

Now 195!!!

Robbietl

+1

level 42

Jan 15, 2018

47, 49, 4, 10, 15, 16, 27, 30, 48, 36, 38, 39, 28, 46, 34, 50, 42, 40, 33, 44

jayjay068

+1

level 25

Jun 15, 2016

You can't win :(

IightsIash77

+1

level 40

Feb 17, 2017

47, 49, 4, 6, 25, 46, 38, 26, 50, 40, 30, 45, 44, 24, 36, 28, 34, 48, 42

zysiex

+1

level 20

Sep 21, 2017

47, 49, 35, 21, 39, 33, 27, 45, 26, 46, 38, 18, 42, 34, 30, 50, 28, 44, 36, 24, 48, 40 - taking always the biggest number with only two factors

Saharan

+1

level 32

Jan 9, 2018

47, 10, 15, 20, 30, 35, 40, 45, 50, 24, 34, 39, 44, 28, 38, 48, 42, 36, 46

Gandalf9010

+1

level 47

Jun 15, 2016

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

Gamer1162

+1

level 64

Jun 15, 2016

I beat him by 7, I feel satisfied

Instrumental

+1

level 53

Jun 15, 2016

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.

Saharan

+1

level 32

Jan 9, 2018

I also wonder what is the biggest win you can achieve...

sf49ers

+1

level 79

Jun 16, 2016

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...

jmellor13

+1

level 56

Jun 16, 2016

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.

Arp2600

+1

level 74

Jun 16, 2016

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

Quizzer6794

+1

level 58

Jun 16, 2016

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

Liverpool03

+1

level 54

Jun 19, 2016

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

geographyisthebestsubject

+1

level 37

Jun 20, 2016

Very creative and fun quiz!

Arp2600

+1

level 74

Jun 20, 2016

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...

Arp2600

+1

level 74

Jun 20, 2016

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.

Arp2600

+1

level 74

Jun 20, 2016

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.

Arp2600

+1

level 74

Jun 20, 2016

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.

Arp2600

+1

level 74

Jun 20, 2016

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.

Arp2600

+1

level 74

Jun 20, 2016

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.

Arp2600

+1

level 74

Jun 20, 2016

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.

Arp2600

+1

level 74

Jun 20, 2016

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

eattrig

+1

level 58

Nov 22, 2017

Nice write-up @Arp2600. I've confirmed that your solution is optimal by writing and running a brute force algorithm. It did in fact come up with the exact answer you stated here.

joeythelemur

+1

level 73

Jul 18, 2016

Third try, won by 145! Fun game!

Jen81

+1

level 33

Jul 22, 2016

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!

Jen81

+1

level 33

Jul 22, 2016

Yup, lost by 199!

BAMALAMIAN

+1

level 34

Aug 15, 2016

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

wtstoudt

+1

level 66

Aug 16, 2016

But can you tie?

JBlouw1850

+1

level 47

Oct 31, 2016

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

ChaosQuizzer

+1

level 21

Aug 24, 2016

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.

Azerk

+1

level 20

Aug 25, 2016

aww

Anirudh123

+1

level 17

Sep 27, 2016

I DID WITH 341 POINTS

GeneraliGeeks

+1

level 65

Oct 5, 2016

Eh?

SuperSans321

+1

level 6

Oct 6, 2016

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

Matthew07

+1

level 35

Oct 12, 2016

Finally won 693-582

MyMindWentBlank

+1

level 48

Oct 15, 2016

Is your score the sum of your selections?

KoljiVriVoda

+1

level 67

Oct 17, 2016

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

nmaec

+1

level 45

Oct 20, 2016

Bet him on the 3rd try by 23

Alex99

+1

level 37

Oct 21, 2016

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

Alex99

+1

level 37

Oct 21, 2016

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

Arp2600

+1

level 74

Jun 27, 2017

As strange as it can seem, the worst loss (683) is obtained by using the winning strategy for a 25 grid.

TheNerdKid351

+1

level 42

Oct 29, 2016

Is this even possible? Best score: lose by 65

karkatfan12

+1

level 7

Nov 1, 2016

OMG i won
(by 43)

3275

+1

level 26

Nov 26, 2016

win 498
loss 684

Rougecompany

+1

level 42

Dec 12, 2016

I lost by just 17... So close

catlover2496

+1

level 40

Mar 10, 2017

Same

Soccerstud

+1

level 34

Dec 15, 2016

Beat it by 647

eversj

+1

level 16

Dec 15, 2016

Beat it by 647

danny11mcl

+1

level 23

Dec 15, 2016

beat it by 647 also

BlorbyFuncho83

+1

level 44

Dec 16, 2016

I beat him by 15 by randomly guessing numbers. WOW

BlorbyFuncho83

+1

level 44

Dec 16, 2016

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

yobhdgmu

+1

level 39

Dec 17, 2016

lost by 83

Tomasquilmes

+1

level 3

Dec 27, 2016

I won by 1 (638-637)

DrDragon

+1

level 44

Jan 5, 2017

Beat him by 75

Sophia458

+1

level 21

Jan 22, 2017

Weird gameπ

catlover2496

+1

level 40

Jan 31, 2017

I beat the taxman by 17! 646-629

meyerjp

+1

level 36

Feb 24, 2017

I won by 115 on my third try. No real strategy, just picking high numbers with minimal factors.

DasCreamy109

+1

level 52

Dec 4, 2017

There is your strategy, bud.

QuizBeater101

+1

level 7

Mar 4, 2017

I lost by only 75, by picking 47, 46, 49, 9, 36, 38, 39, 42, 50, 48, 34, 45, 33, 44, 40 (in that order). I know that the best first number is 47 because the score will become 47-1, the biggest advantage.

QuizBeater101

+1

level 7

Mar 4, 2017

SPOILER ALERT! THIS COMMENT REVEALS A WAY TO BEAT THE TAXMAN BY 159!
I beat the taxman by 159! I used 47, 49, 35, 21, 33, 22, 44, 42, 18, 36, 46, 39, 45, 38, 34, 30, 48, 40, 50

SwampyThrowerBoy

+1

level 32

Mar 8, 2017

Got a cheeky 738-537 win. AFTER ABOUT 20 TRIES!!!!

redboter

+1

level 28

Mar 17, 2017

I finally got it but barely. Only won 665-610.

Alberta

+1

level 12

Mar 18, 2017

I was winning at first but then lost by 297

ChanelSea

+1

level 54

Apr 1, 2017

47, 49, 4, 6, 25, 46, 48, 38, 26, 50, 40, 30, 45, 44, 36, 28, 34, 42
Beat him by one this way

JoJOjO13579

+1

level 5

Apr 6, 2017

I lost by 391

RileyB

+1

level 13

Apr 24, 2017

I beat it by 639

Jarl5

+1

level 55

Apr 25, 2017

Dangit! Closest I can get is losing by 37

Sirlandlord

+1

level 65

Apr 30, 2017

At last, I beat him by 77. I think I could have done better.
As a tip, start with 47 of course and then probably 49 35 50 15 45

geographyman19

+1

level 34

May 11, 2017

i finally won on like my 15th try i beat the taxman by 5

idude

+1

level 18

May 18, 2017

I lost by 1 after the following sequence
47, 49, 4, 6, 25, 26, 46, 50, 45, 40, 24, 42, 33, 38, 34, 48, 36, 44

triviabrain

+1

level 20

Jul 8, 2017

I beat him by 21

Tomasmental

+1

level 80

Jul 15, 2017

I beat the taxman 715-560. between that and my recent improvement on levels, I now need too be a 70 or + level player to fulfill my expectations in this website.

SwiftNinjaD52X

+1

level 13

Jul 15, 2017

i lost by 403 and then 355

DarthCaedus66

+1

level 14

Jul 31, 2017

I was 75 points away from my first win ever.....

DarthCaedus66

+1

level 14

Jul 31, 2017

Now 17

Neptune777

+1

level 55

Aug 13, 2017

Closest is -17 :((

3275

+1

level 26

Sep 6, 2017

lost by 7

atomicbomb1213124124

+1

level 17

Sep 14, 2017

The best win is 808-467 winning by 341 points with 47, 49, 35, 21, 39, 33, 26, 46, 38, 34, 27, 18, 42, 28, 45, 44, 36, 30, 50, 40, 32, 48
The worst loss is 296-979 losing by 683 points with 23, 25, 15, 21, 14, 22, 20, 16, 18, 24, 26, 38, 34.
This is done by using the "winning" strategy as if it was a 25 number board.

kogatora

+1

level 47

Jan 6, 2018

so the best winning strategy is to tell the taxman he has to pick and convince him you only have half the numbers you do... sounds like real life

kogatora

+1

level 47

Jan 6, 2018

ps. i've seen this on other sites and 808 is the most likely best score stated there (haven't seen a complete proof against a higher one but seems unlikely there is one), kudos for working it out!

atomicbomb1213124124

+1

level 17

Feb 20, 2018

I don't understand what you mean by that but the using the strategy for a 25 number board is the way to lose by the most.

Arp2600

+1

level 74

Mar 1, 2018

Yes, that's what I stated above (three months before you :p). It's mostly because, playing like that, you prevent yourself from taking any high number (for example, eliminating 25 with 5 gives the 50 to the taxman).

ZaxxaOfficial

+1

level 30

Sep 14, 2017

You know how when a number is eliminated? It would make it a lot less confusing if you crossed out the numbers that the players get in a color (say, green) that is different from the ones that the taxman gets (say red). Just a suggestion.

Austin1229

+1

level 23

Sep 21, 2017

FINALLY WON, only by 49 but still

nmaec

+1

level 45

Sep 22, 2017

Beat the Taxman by 31

SweetCorn

+1

level 42

Sep 29, 2017

I'm honestly a really bad at math, so a win by 5 points is good enough for me.

SweetCorn

+1

level 42

Sep 29, 2017

"a really bad at math".
I'm also bad at spelling it seems.

catlover2496

+1

level 40

Sep 30, 2017

47, 49, 25, 39, 26, 8, 50, 45, 40, 36, 22, 28, 32, 34, 38, 42, 46, 48 -
I WIN BY 35. 655-620.

tailsfan11

+1

level 52

Oct 6, 2017

W by 9, 642-633. I'm so proud of myself!

bubby33

+1

level 3

Nov 1, 2017

I seem to have double or even triple the score of the taxman before I click the last number, and when I click the last number, I lose for some reason.

RPHXX

+1

level 55

Nov 11, 2017

Because he also gets all Numbers that you haven't used.

joy4u

+1

level 6

Nov 3, 2017

My score reads '435-217'. What does that mean?

RPHXX

+1

level 55

Nov 11, 2017

You got 435 Points and he got 217.

RPHXX

+1

level 55

Nov 11, 2017

I did it by 81.

kyre510

+1

level 20

Nov 19, 2017

Took about 21 tries lol

wijerathne

+1

level 7

Nov 30, 2017

(not a lie ) i tried 2 times and beat the taxman the 2nd time by 209!

KataJ

+1

level 41

Dec 7, 2017

won by 5, took way too long

Anshul

+1

level 33

Dec 12, 2017

Lost 628-647, my closest try!

Anshul

+1

level 33

Dec 12, 2017

Now beat him 740-535

Anshul

+1

level 33

Dec 27, 2017

Now beat him 779-496

JJBE123

+1

level 10

Dec 27, 2017

Won by 15!

Anshul

+1

level 33

Dec 27, 2017

My biggest win is by 283 points 779-496 :)

Lusture

+1

level 15

Jan 27, 2018

WON BY 96!!!!!!

Screamrearer

+1

level 20

Feb 9, 2018

47, 49, 4, 6, 25, 46, 38, 26, 50, 40, 30, 45, 44, 24, 36, 28, 34, 48, 42, 44. Win by 49 points

Screamrearer

+1

level 20

Feb 9, 2018

47, 49, 35, 21, 39, 33, 27, 45, 26, 46, 38, 18, 42, 34, 30, 50, 28, 44, 36, 24, 48, 40 Win by 325 points

Celloninja

+1

level 41

Mar 2, 2018

My first win:
47, 49, 42, 35, 28, 45, 39, 33, 48, 44, 40, 36, 50, 46, 38, 34
By 33

Gonagi

+1

level 11

Mar 2, 2018

Thank you for introducing the Game.its fun.but I lost by95

Gonagi

+1

level 11

Mar 2, 2018

Thank you to screamrearer.325!

manOFsteel

+1

level 31

Mar 4, 2018

You have to start off with 47 49 in order to win. I won by 159

foxyfab

+1

level 32

Mar 9, 2018

lost by 203. dont quite get it, but maybe bc the explaination is in English >.

3ommy25

+1

level 10

Mar 14, 2018

YES won by 13 after 30mins!

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