Your goal is to put the letters M, R, and P in the board so that each letter appears once in every row and every column.
You are told what letter you see first from the border.
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Solution:
Here is Seth Cohen's excellent explanation:
Column 1: R has to go at the bottom. Otherwise, the P and M can't fit above it (they have to be above it, because R is seen from the bottom).
Row 1: P and R have to go on the far right, in that order. No other way for that row to work with the things that are seen from the top.
Row 4: M has to go on the left. It can't go in position 2 or 3, because M is seen first from the top, and there wouldn't be room below the M for the P and R. It
can't be in 4 or 5, because M is seen from the left, and there wouldn't be room to the M's right for P and R.
Column 4: M goes on bottom. Can't be position 2 (from bottom), since there's only one M in the row. Can't be position 3, because R would have to go to its right,
putting 2 R's in right column. Can't be in position 4, because there wouldn't be space for R in column.
And the rest...I looked at column 3 and asked where R went. I tried it in the middle, and everything just worked.