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Est. 1998 — 27 years of woodworking knowledge

Abingdon, VA – Tree Cutting & Portable Sawmill

Friday puzzle -- cut lines

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Friday puzzle -- cut lines

#1

Friday puzzle -- cut lines

You are given a 6" x 12" piece of card stock with the center marked. You are to draw four line segments, each one extending from the center to one of the edges or corners, with each line segment being an integral number of inches long. These lines need to be drawn such that you can pick two of them to cut along, to create a piece of card stock of any area that is an exact multiple of six (6,12,...,66).

What is the sum of the length of the four segments?

I am aware of two solutions (other than rotations and reflections), which have the same total length. Anyone find more than two solutions?

Re: Friday puzzle -- cut lines

#2

Starting piece is rectangular

Re: Friday puzzle -- cut lines

#3

Re: Friday puzzle -- cut lines

Not sure that I follow this completely:

Are we looking for numbers of ways to draw the lines, Or numbers of ways to draw the lines with the same total length?

Do all possible cuts (using two of the 4 drawn lines) have to result in an area with a multiple of 6?

Re: Friday puzzle -- cut lines

#4

Clarification

Looking for A way to draw the four lines. Then answer is the sum of their lengths.

I think there is only one possible answer (sum of lengths), but it can be gotten with two slightly different set of lines.

All possible multiples of six (1-11) have to be achievable by selectio of two of the lines to cut.

Re: Friday puzzle -- cut lines

#5

I see two ways

The answer is in a Steely Dan song.

Re: Friday puzzle -- cut lines

#6

:-)

Had to go to Google to confirm the answer!

I think those are the only two ways to do it.

This one was probably easier to solve than to state, once you put pencil to paper.

We'll try a harder one next week!

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