Letters like this motivate me

I recently got an email titled “Great Site !!! ” Emails like this make me want to put more effort on math 24 game and put more content on this site.  With Manuel’s content, I post the edited email below:

Hello, my name is Manuel, i am from Barcelona, Spain.

First of all  would like to thank you for all the information i got from your site.

24 is a great game a friend of mine teach me two weeks ago.

I am just learning Java and coded the game. Brute force algorithm building all permutations given for numbers, adding all permutations for signs and finally adding all possibles parentheses. Then evaluating each possible solvable. Founding all solutions.

In the other hand in Rosettacode page i looked carefully all codes, (did not found Java which really surprise me)  but what surprise me the most was that all codes there, work like mine, brute force.

I will continue in summer, after my final exams, trying to do my best with the algorithm.

Keep this nice site up.

Cheers !!

Difficulty level of a quadruple in 24 math game

Given two quadruples, say (1,2,3,4) and (7,8,9,10), which one is easier for a human to get a solution?

Looks to me 1,2,3,4 is fairly easy, 4×3×2×1, meanwhile, 7,8,9,10 is solvable with  9×8/(10-7) , but slightly more difficult in my opinion.

Turns out (7,8,9,10) has only one solution shown above, while (1,2,3,4) has three distinct solutions  (3+2+1)×4, 4×3×2×1 and (4+2)×(3+1).

It seems to me there are three factors that decide the difficulty level of a solvable quadruple:

1) number of solutions, the more the easier.

2) type of operations, I cannot say for sure that the order from easiest to most difficult is + – × /, but I know 13/7 is as hard as it comes.

3) size of the numbers, the smaller the easier (it’s easier to do 4 + 3 than 13 + 7, slightly)

Obviously the best way to really figure it out is to develop a game, let millions of people play and collect their reaction time to each quadruple. That’ll be awesome and probably my ultimate goal.





New solver

Now I can finally rest in peace.


It’s uber fast as I pre-computed all the solutions and store them in a long string. So instead of let a CGI do it in real time. I let a piece of java-script code search for the solutions in the said long string.

the Ultimate Solver

Now I am finally done with the new solver. It gives no gimmick solutions. All solutions are entirely distinct from each other according the the rules on the theory page. And I believe my theory is pretty close to how humans judge distinctiveness among different solutions.

Now what? Now I am going to go read Anthony Bourdain’s “Kitchen confidential”.

New Solver!

Now the theory is complete!


Check out the new solver which gives no gimmick solutions. Pretty much all solutions are reasonably distinct. Except solutions like 4 * 6 *7 / 7 and 4 * 6 + 7 – 7 are treated as distinct solutions.

I think it’s debatable if they are different and I will just leave them as is.

Will update all other pages to reflect the completeness of the solver.


Edit: On second thought, 4 * 6 * 7 / 7 and 4 * 6 + 7 – 7 should be treated as the same solution, will finish this over the weekend.


CSS float

If you view the site on your Chrome/Safari/Firefox browser, you see what the site is designed to look like. IE on the other hand, acts up on my CSS file (which is stolen from nearlyfreespeech).

Tried a couple of things and gave up. My hack on the problem is to change all the floating objects in the CSS to fixed positions.  So, go download a Chrome or Firefox browser. IE blows.

Almost done, I will redirect the ocf.berkeley links here over the weekend.


The site

I have been researching for the right webhosting service (and domain registration all that) for a while. Of course with the SOPA drama, Godaddy is the first thing that I would not consider.

After reading a bit of the comments on reddit,  I was convinced that  nearlyfreespeech might be worth trying. So far so good. And I actually like the layout on their site. And I have hence used their css file. So don’t be surprised that 24theory looks just like nearlyfreespeech.