# What is the maximum number of allies that you can have in this scenario?

There is a military/diplomatic crisis, with many sides involved. Your goal, as an uninvolved party now entering the conflict, is to get as many allies as you can. You make an ally by supporting a given side (among A, H, I, M, R, S, T). But it's not that simple. There are conditions:

• You must either support S or A, neutrality is NOT an option.

• If you support R, then you support A and I.

• If you support A, then you support I and do NOT support M.

• If you support S, then you support M and do NOT support A.

• If you support I, then you do NOT support S, but support A.

• If you support M, then you support H.

• If you support H, then you support M and I.

• If you support T, then you support M and do NOT support A.

• The puzzle is nice, but could you possibly change the setup/scenario? It would be easy to give essentially the same puzzle/deductions without referring so casually to things that really cause thousands of real people to die. Commented Jan 11, 2020 at 16:14
• We do puzzles here, not politics. The part that belongs on this site is the puzzle, the real world situation can change and is not an essential part of the puzzle.
– Bass
Commented Jan 11, 2020 at 16:52
• The community decides how this site is run. I am confident that the general consensus is to keep puzzles enjoyable by everyone. This is not the place for conflict
Commented Jan 11, 2020 at 17:00
• @Adam I still would like to hear what exact rule my original wording of the puzzle supposedly broke. Commented Jan 11, 2020 at 17:09
• The original version of the puzzle didn't break a rule, just as a puzzle full of spelling errors and typos wouldn't break a rule. But the new version is better, just as a spelling-corrected puzzle would be better than one full of errors. The person who made the original spelling mistakes might be (to use your own word) stubborn and not want them fixed, but they probably still would be and the world would be a slightly better place for it. Commented Jan 11, 2020 at 22:30

First notes:

A and I are connected (if you support one, you must support the other). Same with M and H.

Now,

if you support M and H, you must support I and A, but that means you do not support M. Contradiction, so you cannot support M or H.

Therefore,

you cannot support S or T, since that means supporting M.

That leaves only

A, I, and R, all of which you can support without supporting any of the others.