24Guru User's Guide

11. Adjusting UI Layout, Background Image or Background Music  Contents  A.2 Accelerator Keys

 

Appendix

 

A.1 Irrelevant Solutions


. When you check for answers of a question, 24Guru will provide all irrelevant solutions under current rules for this question.

. Where you check the complete list of all solutions, 24Guru will provide all irrelevant solutions for all questions under specified rules.

. In a World Cup game, or in training or training game while current Difficulty Level is higher than "Beginner", you are required to submit 2 or more irrelevant answers for questions with more than 1 answer.
 

Similar Solutions and Same Solutions

Similar Solutions Accepted by 24Guru

 

Similar Solutions and Same Solutions

There may be many solutions for one question. Some of them are same as or similar to some other.  Only irrelevant solutions are meaningful. Following 4 rules are involved in defining irrelevant solutions by 24Guru. First three 1-related rules define similar solutions, the fourth defines same solutions. Irrelevant solutions are valid solutions of the same question that are not similar to or same as each other. If several solutions are same or similar solutions, 24Guru only provides solutions of the simplest/most common form, which is listed as "Recommended Form" below. Though 24Guru can recognize correct solutions of any form, to avoid possible errors in submitting multiple answers which are same as or similar to each other, you are recommended to submit only suggested form of answers in training or games.


a) Similar Solution 1Calculation 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: if an expression (exp) evaluates to 1, 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.

Ex

 

          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)

 

Similar Solutions Accepted by 24Guru

Except for the 3 obvious similar solutions above, there are still 2 kinds of similar solutions where new solutions can be found from solutions already known. These similar solutions are not as obvious as the 4 kinds above, to avoid unnecessary arguments, 24Guru accepts these "similar solutions" as irrelevant solutions. If you meet them in a 24 game, or just play it with your friends, you can decide according to the rule in your game whether you should submit them as different solutions. If there is no clear description, we suggest you seem them as the same solutions.

1)  2 numbers make 24, other 2 are just same

This is a special case of the second form of Similar Solution 2. It's described separately here because it provides more similar solutions:

a) Eliminate the 2 same numbers by any complementary operations (+n, -n), (*n,  /n), (^n, ^^n) with either of the other 2 numbers.

b) After the other 2 make 24 in the first round, eliminate the 2 numbers by complementary operations.

Ex - 4,6,7,7:

 

 -> (4+7-7)*6

 -> (4*7/7)*6

 -> (4^7^^7)*6 (= 4^(7/7)*6 similar to 4*(7/7)*6)

 -> 4*(6+7-7)

 -> 4*(6*7/7) (same as (4*7/7)*6)

 -> 4*(6^7^^7)(->4*6^(7/7))->4*6*(7/7)->(4*7/7)*6) -> 4*6+7-7 -> 4*6*7/7 (same as (4*7/7)*6)

 -> 4*6^7^^7(= 4*6^(7/7) similar to (4*7/7)*6)

 

2) Result of some operation on 2 numbers is same as one of another number, and the 3 (the result, the one same as the result, and the other) make 24

The operation to make the result same as another number can exchange its place with that same number to make a pair of valid solutions:

Ex - 4,7,5,9:

 

 -> 4*7-(9-5)

 -> (9-5)*7-4