Logical Larry was upset to learn that his recent submission to a logic problem magazine had multiple solutions. As it turns out, the magazine editor accidentally omitted one of his clues.

Here is the clue as it was printed:

Four children (Betty, Bobby, Billy, and Brian) enter a store selling bikes, balls, and balloons, each of which come in blue, brown, or beige.

From the clues below, determine what each child purchased:

1. Betty did not purchase a balloon.

2. Bobby and Billy purchased the same color item, which was not brown. Betty and Bobby purchased the same item.

3. Betty thought it best to purchase a brown item.

4. Brian is the only one who purchased both his item and his color.

5. A brown ball was not purchased. Neither was a blue bike.

The missing clue should have read, "A balloon was not purchased by _________" However, Larry cannot remember what should be in the blank to make the problem solvable.

What should be in the blank?

(In reply to Not solvable by Alec Lanter)

Agreed.

If the answer reads "A balloon was not purchased by Billy," Billy can buy either a beige bike or a beige ball, and Brian can but either a blue ball or a blue balloon (they just can't both get the ball).

If the answer reads "A balloon was not purchased by Brian," Brian gets the blue ball, but Billy can get either a beige bike or a beige balloon.

And of course if the clue names anyone else then it was worse then usless.

This puzzle can't be solved. Perhaps it was missing a second clue?

Posted by Sam on 2004-04-27 14:50:59