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Monday, May 24, 2010

The Professor's Wooden Measuring Stick

Professor Egghead was accompanying a colleague on a remote archaeological expedition.  On the first day of the dig, however, he was surprised to discover that he had forgotten some of his tools at home.  Most important of his missing tools was his ruler, used for measuring lengths of small objects uncovered at the dig site.  He was able to find a straight, blank wooden stick that measured exactly 10 inches and borrowed a ruler from one of the other members of the team to make marks on his stick to create a ruler of his own.  To keep things simple the professor wanted to make as few marks on his new ruler as possible.

What is the fewest number of marks the professor could make on the stick so that he could still accurately measure any whole number length from 1 inch to 10 inches?  For instance, placing a mark 1 inch from one end would allow the professor to measure 1 inch and 9 inches.

It's 4, right?

4 marks takes you up to 5 inches if you skip the mark at 2 inches.

You can then measure 2 inches using the marks between 3 and 5.

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Although, come to think of it that leaves us shafted when it comes to measuring 8 inches. Bugger.

How about this then - put marks at 1, 2, 3, and 6. (4 marks).

You can measure 4 inches using the marks between 2 and 6, and 5 inches using the marks between 1 and 6