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Consider a standard $8\times 8$ chessboard where a pawn is placed on each of the squares $d1,d2,d3,d4$ . Dissect the board into $4$ congruent pieces (reflections are allowed) such that each piece contains exactly one pawn.

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What are your thoughts? –  Henning Makholm Dec 22 '12 at 19:31
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Do the pieces have to be connected? –  Mark Bennet Dec 22 '12 at 19:33
    
@MarkBennet: The problem sheet on which I found this problem is ambiguous but since the original formulation of the problem talks of a field which is supposed to be partitioned among 4 brothers I guess one should assume that the parts should be connected. –  Dominik Dec 22 '12 at 20:36
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Print out the diagram and draw the lines ... Top pawn has to be joined to the square to the left. Square to right of top pawn needs to be joined down then left ... other central squares follow by symmetry. –  Mark Bennet Dec 22 '12 at 23:07
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Try spirals that grow from each corner simultaneously. –  Greg Martin Dec 23 '12 at 1:27
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1 Answer

up vote 4 down vote accepted

I think growing spirals from each corner simultaneously does the trick.

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I edited your image to make it easier to see the pieces, you can use it in your answer if you like: i.stack.imgur.com/DUrtX.png –  Rahul Jan 3 '13 at 0:50
    
hooray, I was hoping someone would improve the picture - and you did even better than I'd hoped! Thank you –  Greg Martin Jan 3 '13 at 17:51
    
I think this problem goes back to Dudeney's Amusements in Mathematics. –  Gerry Myerson Jan 4 '13 at 2:46
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