3.1 Standard Rule

3.2 Advanced Rule

3.3 J, Q, K Enabled

3.1 Standard Rule

A "24 points" game, or a "24" game, starts with 4 positive integer numbers, each ranging from 1 to 10 (or 1-13, if J, Q, K are enabled). For example - 1, 3, 5, 7. The goal of the game is to find a procedure, through 3 rounds of arithmetic operations (addition, subtraction, multiplication or division), where the 2 operands are numbers from the 4 starting numbers (each number can be used once and only once), or the result of a previous operation. At the end of the 3 rounds of operations, a final number will be created. If you find a procedure to make the final number as 24, then you win. A possible procedure for the above question is: 

          Round 1: 3-1 = 2;

          Round 2: 7+5 = 12;

          Round 3: 2*12 = 24;

We can also describe the rule in another way - to form an arithmetical expression by the 4 provided numbers; each number must be used, and must be used only once; only 4 kinds of operations - addition, subtraction, multiplication, or division - can be used; you can use parenthesis if you want at suitable time. What you are supposed to do is to find an expression under this condition which will evaluate to 24. For example, for the above question, one of the solutions is:

          (3-1)*(7+5)=24.

3.2 Advanced Rule

Though not popular everywhere, in some games, 2 other operations are allowed to be used to form your expression which can evaluate to 24 - power (expressed as n1^n2) and root (expressed as n1^^n2). There are some configurations which cannot be calculated under standard rule, but can get through when either or both of the 2 new operations are permitted. For example, there is no solution for (1,1,2,5) under standard rule, but under advanced rule, we still can get 24 by

          (5^2-1)*1=24.

3.3 J, Q, K Enabled

It seems the game of calculating 24 is originated from card games. Usually only A(1) and 2-10 are involved in calculating 24. In some place, J, Q and K are also allowed. Under some rule, when J, Q, K are allowed, they all equal to 10. Under some other rule, J, Q, K can mean 11, 12 and 13 respectively. In 24Guru, when you check on "Enable J, Q, K", 11, 12 and 13 may appear in the questions.