# What is the value of the letters?

What is the value of the letters A and B in the figure down below? The square and the circle are independent from one another, i.e. they are solved independently.

Here follows my train of thought:

For the square I first noticed that the middle row sums to 30 and that the main diagonal also sums to 30. Then I began filling in the empty squares such that each row, column and diagonal sums to 30, but doing this I end up with that A can be any value between 0 and 12.

For the circle I noticed that the sum of each piece is 1 greater or smaller than the piece straight opposite to it. This left me with B being either 6 or 8.

I think that when you have found the right solution it should be no uncertainty to what the correct value is. This is why I think that my solution is wrong. Edit: The puzzle is from here. It's a geocache myst. In this myst you solve several logic puzzels that in the end give you the coordinates to where the cache is hidden. I have solved all the logic puzzels except the two that I have posted here.

• To make all lines 30 with no number repeated on the same line, A can only be 1 or 11 – Joshua Bizley Jul 30 at 15:48
• Yeah, I was thinking that as well, but you still have the ambiguity of A being either 1 or 11 and not a definite single-value, which feels weird to me since logic puzzels . Do you have any take on the circle @JoshuaBizley? – Turbotanten Jul 30 at 15:55
• Not yet... could it be intended that there are multiple coordinates people have to check? – Joshua Bizley Jul 30 at 16:30
• Is this from an ongoing geocache, or are we to believe the 'found it's? – JMP Jul 30 at 18:57
• I don't know about Myst geocaches (is this a geocache inside the game?!) but real-world geocaches can be found any number of times by any number of people and there's no prize beyond the satisfaction of recording that you found the cache. – Gareth McCaughan Jul 30 at 18:59

For 1:

Using sum of lines=30 and distinct entries on a line, A=1 or 11. But using the equations given at the bottom of the page, A is a single digit, so A=1. However, from the definition of Q (L=1), AB+1 is a divisor of 100 greater than 10, so A=3 (B=8) or 4 (B=6).

For 2:

B is 6. If it was 8, swapping the contents of the 32 cell (make 2 inside, 3 outside), and also the 53 cell, makes the inner circle 1234567, and so if the answer was 8 then the setter would have done just that, and put the 8 on the inside! But they didn't, so the answer is 6.

A more logical explanation:

Alternate segments go +1, (+2,-1), +1, (+2,-1) with their opposite segment.

To say 'Found It!':

E=3, FG=21, CD=24, H=4, IK=10, L=4. From M, A=3, B=8. So now you know!