24Guru User's Guide

3. Rules Contents 5. Difficulty Level and the Training, Comment and Test of Multiple Solutions for One Question

4. The Perfect Irrelevant Solutions Provided by 24Guru

There may be many solutions for one question. Some of them are similar to or just same as some other. Solutions provided by 24Guru are essentially irrelevant to each other. In following situations (we call the first 3 Similar Solutions, the fourth Same Solution), there can be more than one similar solution which can be seemed as the same solutions. We list only the solution which we think is of the simplest/most common form.

a) Similar Solution 1 - Calculation in any one of the 3 rounds is n*1, n/1, n^1(advanced rule), n^^1(advanced rule)

Results for all the 4 are n. Though there may be argument that they are different theoretically, they are at least similar, and CANNOT be accepted by 24Guru as irrelevant answers.

Recommended Form: only submit answers containing n*1, but not n/1, or n^1, or n^^1.
Ex:

2*3*4/1 = 2*3*4^1 = 2*3*4^^1 = 1*2*3*4

For the same reason as above, if an expression (exp) evaluates to 1, then solutions containing *(exp), /(exp), ^(exp) and ^^(exp) are similar solutions.

Recommended Form: in such situation, only submit solutions containing *(exp), but not /(exp), or ^(exp), or ^^(exp).

Ex:

2/(2-1)*12 = 2^(2-1)*12 = 2^^(2-1)*12 = 2*(2-1)*12

b) Similar Solution 2 - 3 of the 4 numbers can make 24, and the other one is 1

This is in fact the extension of the general situation of the above rule. It should be 2 rounds for the 3 numbers to make 24. In such a case, the extra 1 can be eliminated by multiplying it with any number (original number or result number) at any of the 3 rounds.

Recommended Form: submit solutions where 1 multiplies the resulted 24 after it was created in previous rounds.

Ex:

1*5+7+12 = 1+1*7+12 = 1+7+1*12 = 1*(5+7)+12 = 5+1*(7+12) = 12+1*(5+7) = 1*(5+7+12)

For the same reason as above, if 2 numbers make 24, other 2 make 1, the 3 solutions created by multiplying the expression resulting in 1 with any of the former 2 numbers before they make 24, or multiplying it with the resulted 24 are similar solutions.

Recommended Form: submit solutions where 1 multiplies the resulted 24 after it was created in previous rounds.

11*(4-3)+13 = 11+13*(4-3) = (11+13)*(4-3)

c) Similar Solution 3 - Calculation in any one of the 3 rounds is 1^(any expression) or 1^^(any expression)

Results for the 2 form are both 1. No actual new solutions can be created if other parts are same or similar.

Recommended Form: submit solutions containing 1^(any expression), but not 1^^(any expression)

Ex:

3*(7+1^^9) = 3*(7+1^9)

d) Same Solution - Solutions which can be derived through algebraic procedure from each other are same solutions
Recommended Form: there are many different forms of same solutions. Please only submit solutions of the simplest/most common form based on specific situation.

Ex1: n2+n1+n3+n4 =n3+n1+n4+n2 = ... = n1+n2+n3+n4
Ex2: n2*n1*n3*n4 =n3*n1*n4*n2=((n1*n2)*(n3*n4)) = ... = n1*n2*n3*n4
Ex3: (n2+n1)/n3/n4 = (n2+n1)/(n3*n4) = ... = (n1+n2)/n3/n4
Ex4 (part): n1^n2^n3 = (n1^n2)^n3 = n1^(n2*n3)
Ex5: (8-12)^2+8 = (12-8)^2+8 (this case can be seems as similar solution under strict analysis)

Other solutions that are not listed can be explained in a similar way. For more details about irrelevant solutions, please read A.1 Irrelevant Solutions.

Developers of 24Guru designed strict and delicate procedures for 24Guru to go through cross-verification against all theoretically possible solutions for all 24 problems under different rules. All minor bugs involved in solution have been dug out and fixed through such procedures. Now we have good reason to believe, since version 1.1, the solution engine of 24Guru has been perfect -the irrelevant solutions provided by 24Guru for each 24 question under standard and advanced rule are the theoretically complete list of irrelevant solutions it can have.