There are six boxes containing 5, 7, 14, 16, 18, 29 balls of either red or blue in colour. Some boxes contain only red balls and others contain only blue.

One sales man sold one box out of them and then he says, "I have the same number of red and blue balls left over."

Which box is sold out?

OK, I'm 0 for 2 on my last 2, but 2 for 2 on the first two, so here goes.

Adding all the balls up, you come up with 89 balls. Subtracting the number of balls for each box has to be an even number, otherwise you wouldn't have the same red and blue. This eliminates 3 of the boxes. Then you have to figure how you could add up to the half number remaining -- you like my poor English?

Like so
89 - 5 = 84
89 - 7 = 82
89 - 14 = 75, but odd, so no good
89 - 16 = 73, also odd, so no good
89 - 18 = 71, also odd so no good
89 - 29 = 60

With the remaining balls, you have to add up to half of one of the above, 41, 42, or 30. 30 works out well, because 7 + 5 + 18 = 30, and 16 + 14 = 30. The others don't add up. Therefore, the box of 29 was sold.

Posted by Lawrence on 2003-08-24 06:39:18