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| (1) Posted by Hauke Reddmann [Sunday, Aug 25, 2013 14:21] |
Chessboard cut&paste puzzle
How many pieces do you need to cut up a 6*6 and 8*8 chessboard
and rearrange it to a 10*10 one?
- The chessboard has no "backside", like a RL one. So no turning
over of the pieces! (Which invalidates the solution given on the internet -
http://math.ucsd.edu/~wgarner/personal/puzzles/joiners_problem_sol.htm)
- And of course the chessboard pattern shall remain.
5 pieces are almost trivial, but can you do it with 4? (You don't have
to make your cuts along the field borders. But it probably helps :-)
Hauke
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| (2) Posted by Kostas Prentos [Sunday, Aug 25, 2013 19:50] |
It is rather easy to do it with 4 pieces, if you keep 6*6 as one piece. Then, you attach a 6*4 piece on one side (let's say north) to get a 6*10 rectangle and the remaining 2*4 and 8*4 on the other side (west or east) of the 6*10 rectangle. There may be other solutions with 4 pieces, but it seems impossible to do it with less pieces.
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| (3) Posted by Jacques Rotenberg [Sunday, Aug 25, 2013 22:29] |
You may have a problem with the color of the squares...
But I don't know if this was is the question...
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| (4) Posted by Kostas Prentos [Sunday, Aug 25, 2013 22:56] |
I did not read the question carefully and I did not think about the colors of the squares. The solution I suggested does not give a checkered 10*10 board, so it is wrong. It does not seem so easy anymore...
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| (5) Posted by Georgy Evseev [Tuesday, Aug 27, 2013 09:57]; edited by Georgy Evseev [13-08-27] |
Solution (I do not know how to hide it)
From 6x6 board cut a square c1-c4-f4-f1-c1.
From 8x8 board cut a part a3-a8-d8-d5-b5-b3-a3.
I hope you will be able to construct a 10x10 board from these parts. No part rotation needed.
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| (6) Posted by Hauke Reddmann [Tuesday, Aug 27, 2013 11:15] |
Surplus for the graphically challenged (like me):
http://imgur.com/LvhcvY9
THX, Georgy!
Hauke
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| (7) Posted by Kostas Prentos [Wednesday, Aug 28, 2013 08:12] |
Lovely solution! Good job, Georgy!
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| (8) Posted by Pietro Pitton [Thursday, Aug 29, 2013 00:27] |
Boris A. Kordemsky in his book "The Moskow Puzzles" (1972 Scribner's) gives this solution of puzzle #162 "A gift for Grandmother":
From 6x6 board cut a rectangle c1-c4-d4-d1-c1.
From 8x8 board cut a part c8-f8-f7-d7-d5-c5-c8.
Kordemsky adds: several solutions are possible.
(I think that Sam Loyd and Ernest Dudeney too created and solved the same puzzle, years before Kordemsky).
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| (9) Posted by Pietro Pitton [Thursday, Aug 29, 2013 01:21] |
Found: Amusements in Mathematics, by Henry Ernest Dudeney (1917)
The book can be freely downloaded at
http://ia600300.us.archive.org/10/items/AmusementsInMathematicspdf/AmusementsInMathematics.pdf
Puzzle #176.—LINOLEUM CUTTING.
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