# Calculation puzzle 012

What's A + B = ? I found A=60 and B=63x4=252, thus A+B=60+252=312; but, source says that's wrong answer.

Source: This question was asked in YTU exam for int'l students in 2018. I have discussed about them in my other posts.

Possible answers are: 158, 204, 112, 148 and 168. Correct one is commented by @Damila below, I don't want to write it here. Thanks.

• Pardon my ignorance @garakchy but what are those directional signs other than the arrow?
– DrD
Jul 27, 2020 at 21:07
• These arrows are part of the puzzle, I believe. Jul 27, 2020 at 21:33
– Stiv
Jul 27, 2020 at 21:40
• Maybe it's not x4 but +45, the other arrows are all sums, aren't they? Jul 28, 2020 at 0:10
• Is the answer 168? Jul 28, 2020 at 2:56

Looks like the apparent relation between the shapes of the arrow heads and the operation they imply is a red herring. And even if they aren't there is no reliable clue as to what open versus filled heads may signify.

The simplest rule is that each kind of arrow means to add a fixed number. Evidence would be that the numbers given never go down and that the black triangle and diamond add to the same increment $$7$$ at two places. The increment needed for the open diamond would then be $$45$$, hence $$A=60;B=108;A+B=168$$.

Occam's razor says the simplest explanation is the best.

The "arrows" can be decoded in a simple and consistent way:
- Black means addition, white means multiplication.
- The number of vertices of the arrowhead seen as a polygon indicates by how much.
In the process you find A = 60, B = 252 and A+B = 312. Just as you did. It is not even difficult to find.

But your source says it is wrong.

There are different possibilities.
- Either this solution works just by chance and there is another better explanation,
- the solution is correct and your source is mistaken.
- there is a typo in the problem statement.

To me it is clear that the 1st possibility is such an extraordinary coincidence that the truth must be in the last 2 explanations.

Among these explanations, it seems more likely that there is an error in the formatting of the problem statement rather than in the transcription of the answer the source refers to.

So my (updated) conclusion is: it is an error in the problem statement.

For example, it is possible the last arrow was meant to have a triangular head. We have enough information to understand that it should mean "times 3". And the solution would be A=60, B=3x63=189, A+B=249.

• Thank you for your efforts. Unfortunately, your answer, like mine, is not even included in the options. I have added the options now. @Damila's answer is correct, I hope he/she writes his/her solution here. Thanks again. Jul 28, 2020 at 8:04
• OK, I saw the intended solution. That would be possibility number 4: there are multiple possible answers but it is intentional. You must use the possible answers to find the correct one. Jul 28, 2020 at 10:48