Date: Sun, 14 Feb 1999 12:46:04 EST
Subject: The Board Problem

Mr. Avery has 3-foot boards and 4-foot boards. If he puts the 3-foot boards in a line, they have the same length as the 4-foot boards put in a line. Altogether he has between 16 and 25 boards. How many 3-foot boards does he have?

HI Avery

Since the number of boards used is at least 16 and you need more 3 foot then 4 foot boards, the number of 3 foot boards is greater than 8.
   The length of the line of boards in feet must be a multiple of 3 and also a multiple of 4. Thus the number of 3 foot boards is a multiple of 4. Since this multiple is more than 8 try the next smallest multiple of 4, 4x3=12. Twelve 3 foot boards is a length of 12x3=36 feet. Thirty-six feet is nine 4 foot boards. Thus, with a total of 12+9=21 boards, you can make 36 feet from 3 foot boards and 4 foot boards.

Jack and Penny


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