Tuesday, August 10, 2010

Monday Puzzle SOLUTION: The Bicycle Thief

The original puzzle.

The only money that matters is the money lost to the thief. Here's Dudeney's solution:

"People give all sorts of absurd answers to this question, and yet it is perfectly simple if one just considers that the salesman cannot possibly have lost more than the cyclist actually stole. The latter rode away with a bicycle which cost the salesman eleven pounds, and the ten pounds "change;" he thus made off with twenty-one pounds, in exchange for a worthless bit of paper. This is the exact amount of the salesman's loss, and the other operations of changing the cheque and borrowing from a friend do not affect the question in the slightest. The loss of prospective profit on the sale of the bicycle is, of course, not direct loss of money out of pocket."

Some may think this is a cheat because of the misdirection of the salesman having to borrow the £25. Since he already had the £15 change from the cashed check, why would he need to borrow £25?

You need to forget that kind of distraction and just focus on the numbers. Why he borrowed the £25 is not important. All that's important is 1) money lost to the thief, and 2) money actually in hand. Keep the focus on the data.


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