Rules of 24 the math game

24 the math game is really one of the most accessible math games out there, especially so before the PC era.

Randomly draw 4 cards from a deck of poker cards, the first player that uses all values on the cards (A = 1, J = 11, Q = 12 and K = 13) and elementary arithmetic operations (+ - × and /) to come up with 24 (or 23.9999....) wins.

Some Examples


The quadruple is {1,2,3,4}. There are several different solutions:
(3 + 2 + 1) × 4, 4 × 3 × 2 × 1, (4 + 2) × (3 + 1) .
Some would say that 4 × (3 + 2 + 1) is another distinct solution. But we disagree.


The quadruple is {4,4,10,10}. There is one solution:
(10 × 10 - 4) / 4
We would all agree that neither ((10 × 10) - 4) / 4 nor ((10 × 10 - 4) / 4) is of any interest.


The quadruple {1,5,11,13} cannot be solved. Unless exponentiation is allowed, in that case, we have 5(13 - 11) - 1.



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