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.





2 thoughts on “Difficulty level of a quadruple in 24 math game

  1. Hi this is great. I am a researcher at Temple University in educational psychology. I am considering using the game 24 as part of an experiment because it is so easy to control the number of possible solutions (thanks to you). However, it would also be great to have actual solution times. Have you made any progress on this?


    • Hi Brian, I am coding up 24 math game with html5. Give me a month or two.

      Then I will collect solution times.


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