# Logical puzzle with possibly two answers [closed]

1+8 = 9
2+6 = 14
5+7=40
1+2+11=?

I arrived at two possible solutions:

1) 23 by A+(AxB) = answer for previous ones and lastly A+(AxBxC) for last one to find the value of "?".
1+(1*8)=9
2+(2*6)=14
5+(5*7)=40
and 1+(1*2*11)=23.

and

2) 36 by the definition of a+b as a+(a*b) from previous equations and then computing left to right for last equation.
1+(1*8)=9
2+(2*6)=14
5+(5*7)=40
So deducing a+b as a+(a*b) and lastly computing from left to right for 1+2+11
step a) (1+(1*2))+11 = 3+11
step b) 3+11=3+(3*11) = 36.

Hence, 1+2+11 = 36.

Which solution is more accurate and why?

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– ACB
Feb 26 at 9:40

There's a third possible answer as well (#2 but go right to left).

Given that the new two-input operator (A op B = A+(A*B)) is not associative in any sense (all three of these approaches give different results), I don't think that any approach is any more or less correct than the others. Heck, it's not even commutative (in general, A op B != B op A).

Another way would be:

A ⊕ B = (A+0)*(B+1)
so
A ⊕ B ⊕ C = (A+0)*(B+1)*(C+2)
and
1 ⊕ 2 ⊕ 11 = (1+0)*(2+1)*(11+2) = 39

There really isn't a single "correct" solution to this question.

We have BODMAS for a reason. The O stands for Order. So do the first operation, get the result, then move on to the second. The intended answer should be 36.