I came across this puzzle while reading Gelfand and Shen's splendid Algebra with my son. The book is full of many other gems, and it is a worthwhile purchase for any math geek.
Measure Twice, Cut Once?
You draw six lines on a stick of lumber to divide it fully into 7 equal lengths.
Then you change your mind and mark twelve lines to divide it up into 13 equal lengths.
Finally you change you mind one last time and cut the wood into 20 equal pieces.
When you are done, the two end pieces will have no marks on them. (Why?) But then you notice something interesting: the other 18 pieces all have exactly one mark on them. Some have a 1/7 mark, and some have a 1/13 mark, but never both.
Why does each inside piece end up with exactly one mark?
What would have happened if you had marked 35 pieces, then 53, then cut 35 + 53 = 88 pieces out of your lumber?
Continue reading if you would ike a hint....Continue reading "A Carpenter's Puzzle"
Sometimes I wonder...
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The latest in mice medical wonders: a major step towards mouse immortality.