How to Solve Marupeke Puzzles

ByJacob Valdez

Marupeke is a grid puzzle invented in 2009 by Naoki Inaba. The rules are pretty straightforward. Simply fill in the puzzle so that there are never more than 2 X’s or O’s in a row, horizontally, vertically, or diagonally. Basically, play Tic-Tac-Toe to a draw against yourself.

This particular puzzle is never really difficult, as the observant player will almost always see the next move, although the black cells can sometimes make seeing the diagonal possibilities a little trickier.

At the beginning, we only have a single square where the placement is apparent. We place an O below these two X’s.
And now, we can place an X here to block these two O’s
This gives us our first diagonal pair to stop, so we place another O.
Just like in Tic-Tac-Toe, one move leads to the next. We put an X here to avoid three in a row.

Starting from this point, we’ll start showing some simultaneous placements so we aren’t being tedious by drawing out each of them one at a time.

First, we block the two diagonal pairs of X’s.  Next, we block the horizontal and diagonal pairs of O’s. And in the third picture, we place an O between the two X’s on the diagonal, and on the top and bottom of the vertical pair.

Can you see the next moves?

Yes, there were quite a few X’s this time. During the middle of the solution, you will want to keep a careful eye out for all the possible blocks.
And toward the end of the puzzle, it will start to slow down again, with only three O’s to place this time.
Now we just place the single X between the O’s on this diagonal.
We block this diagonal with an O,
then an X between these two O’s, and the last move is obvious.
Finally, we have the completed puzzle.

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