Toothpick PuzzleDate: 09/27/2004 at 22:26:17 From: Michael Subject: 3x3 group of squares made up of toothpicks I got this one the other day, and I'm not sure it's possible. If you have a square that is made up of nine little squares, each one toothpick per side, so the big square is three toothpicks per side, can you remove 5 toothpicks and leave 3 squares (of any size necessary)? Taking out 5 toothpicks leaves 19 toothpicks to make 3 squares. I can't figure out a functional way to add 12, 8, 6, 4, 3, 2, and 1 to get 19. I can, but it doesn't seem possible, because some combinations eliminate other possibilities. I don't think the big square (of 12 toothpicks) can be one of the three, because that leaves 7 toothpicks to make two more squares, and making one out of four removes any possibility of making one out of three. If I start with one of the squares being 8 toothpicks, that leaves me 11 to make two squares, so that seems to necessitate another square of 8, but If I do that the only way I can see how, I am left with 3 squares already, and still 3 toothpicks left. Date: 09/28/2004 at 01:53:49 From: Doctor Ian Subject: Re: 3x3 group of squares made up of toothpicks Hi Michael, It's possible that some of the squares can overlap, as in the following diagram: --- --- --- | | | | --- | | | --- --- | | --- --- --- which uses 18 toothpicks (--- or |) to make 3 squares. Does this get you closer to your 19-toothpick solution? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 09/28/2004 at 09:16:37 From: Michael Subject: 3x3 group of squares made up of toothpicks Ah, there it is. Thanks. |
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