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Friday Puzzler -- Plywood square

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Friday Puzzler -- Plywood square

#1

Friday Puzzler -- Plywood square

Alex Y

I have a 4x8 sheet of plywood from which I have cut off pieces needed for another project. I needed a 4x4 right triangle, so I cut from the center of one long edge to a corner. I also needed a right triangle with a long side of 4', so I cut from the center of the other long edge to the center of the cut I made previously. What I have left for my next project is a 4x4 piece with a "roof top" formed by the two 45* cuts.

What is the fewest number of cuts I can make in this odd shaped piece (using my zero-kerf saw, of course) that will allow me to reassemble the resulting pieces into a square?

Re: Friday Puzzler -- Plywood square

#2

Re: Friday Puzzler -- Plywood square

Ed in Leaside

So you're saying you want to end up with a square piece that is 20 sqft?

Re: Friday Puzzler -- Plywood square

#3

Re: Friday Puzzler -- Plywood square

Alex Y

Yes, you've got the picture.

Re: Friday Puzzler -- Plywood square

#4

Re: Friday Puzzler -- Plywood square

Larry Barrett

Fewest cuts = 2. The next question must be how to make these cuts. Part of the answer to that is provided in Ed's question - the resultant square has an area of 20 sqft. So each side of the square must be sqrt20, which is 2sqrt5.

Re: Friday Puzzler -- Plywood square

#5

Re: Friday Puzzler -- Plywood square

Alex Y

Everything you've said sounds right. But I saw exactly what Ed mentioned, and that sqrt(20) = sqrt( 4^2 + 2^2). But that still leaves three obvious possibliities for one of the cuts (four if you count the mirror image), and I still found it difficult.

Did your four cuts result in only three pieces? That was the intent of how to count cuts.

Re: Friday Puzzler -- Plywood square

#6

Re: Friday Puzzler -- Plywood square

Larry Barrett

Yes, 3 pieces. In my solution (I think it is a solution), the two cuts share a point in common (the end of one cut is the beginning of the other).

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