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?
A badge might be cooler, though, and more practical. Being able to show off that you beat the taxman is better than getting points for doing that. Plus, someone could just look at the answers to find the best solution possible, and they would get a lot of points (although the quizzes aren’t safe from that, either)
@SomeoneSomewhere, I disagree. I spent a couple hours trying different heuristics to try to win this, and finally won by like 39 points on my somethingteenth try. I think the badge should be earned by finding a good algorithm, not by perfecting it.
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.
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...
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.
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.
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.
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.
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.
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.
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.
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
Pretty good algorithm, but I don't think it will always be optimal. Basically the algorithm is: take the highest number with only one divisor left on the board. It may work for this specific example but for instance, in the case where only 3, 9 and 27 are in the board your algorithm would lead to us taking 9. The taxman would end up with 3 and 27, and your algorithm would lose. The optimal answer is to take 27 and beat the taxman 27-12, of course. I am not sure if there is any algorithm that will get the right answer for every case.
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.
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!
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.
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
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.
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.
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!
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).
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.
You should add an option to restart/reset the game while playing. This is in case you accidentally clicked on a number and want to restart and try again.
Also if you start on the right row and work down it, the go to the row to the left and work down it, and continue repeating until there is nowhere to click, you lose by 17.
I picked: 46, 10, 15, 20, 30, 35, 40, 45, 50, 34, 33, 32, 39, 38, 36, 44, 42, 48 and I lost by 1 point. 637-638. is there a way to tie or is this the closest someone can get to tie?
I didn’t read the rules properly the first time, I thought that I had aced it but then I lost by 30 and I was so confused. Then I read the rules and died inside.
I tried so many times and my worst loss ever was by 401. I don't know how much worse i can do, but so far i've lost by 401 as my worst loss. I like how you make this game really hard. But I want something else than this and something else thanjust quizzes. Can you make another game that we can play?
49, 33, 27, 46, 35, 45, 18, 39, 32, 44, 48, 50, 40, 34, 28, 38, 42