# 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 Jul 30 '19 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? Jul 30 '19 at 15:55
• Not yet... could it be intended that there are multiple coordinates people have to check? Jul 30 '19 at 16:30
• Is this from an ongoing geocache, or are we to believe the 'found it's?
– JMP
Jul 30 '19 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. Jul 30 '19 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!