The Logical Puzzle - 15 Feb 2005


Draw the shapes that Figure A shows on a paper that has square gridlines, then cut the shapes out. Use the pieces to form a T shape with the proportions that Figure B shows. You might have to think outside the box for this one!


As a reminder, last month's puzzle asked you to calculate the minimum number of cuts required to break a 5-by-8 chocolate bar into its 40 individual pieces. You're allowed to cut only one piece at a time (but not to pile multiple pieces) and only in straight lines (horizontal or vertical).

Most people try to run several different scenarios, first cutting on each horizontal line, then cutting each row vertically, for example. It's confusing to run the different scenarios in your head, so you can easily make mistakes during your calculations and obtain different results for the various scenarios. The varying results you get by mistake can create the illusion that several options exist and that one method requires fewer cuts than another. But the truth is that, regardless of which method you use, you'll always end up making 39 cuts.

The proof uses induction. After no cuts, you have one piece. After one cut, you have two pieces. If you have n pieces and you cut one of them, you get n+1 pieces. In other words, the number of cuts required to get n pieces is n-1. Hence, the minimum—and only—number of cuts required to produce 40 pieces is 39.

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