Good scales have equal arms (arms are the the things that connect the actual scale to the center), but in one grocery stall, the arms of the scale are not equal. Pending replacement, the manager wonders if he can give correct weight this way:

"I'll balance a 1-pound weight on the left with sugar on the right, and then I'll balance the 1-pound weight on the right with some more sugar on the left, and the sugar will add up to exactly 2 pounds."

Will it? What are other (assuming that the above works, it may not) ways of weighing 2 pounds of sugar, if you also have a lead shot with you to help weigh? (Note and hint: The lead shot has an unknown weight. You can make it whatever weight you choose. Remember, the arms aren't equal, and you need 2 pounds of sugar.)

The grocer's method will not be accurate.  Suppose the longer arm is of length "L" and the shorter arm is of length "aL" where "a" is a number slightly less than 1.  One weighing yields "a" units of sugar and the other yields "1/a" units.   a + 1/a is not equal to 2 unless of course a=1.

Posted by Larry on 2004-05-23 10:08:35