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.