Problem of the Week 2

Suppose five bales of hay are weighed two at a time in all possible ways.  The weights in pounds are 110, 112, 113, 114, 115, 116, 117, 118, 120, and 121.  How much does each bale weigh?

 

Alternate Problem 2

Of seven coins, six are the same weight, and one is lighter than the others.  Given a balance with two pans for comparing weights, what is the least number of weighings needed to determine which coin is light?

Of 200 coins, 199 are the same weight, and one is lighter than the others.  Given the same balance, explain how the light coin may be identified in no more than five weighings.

 

Extension Problem 2

Of n coins (n > 1), all are the same weight but one.  Devise a rule for determining the minimum number of weighings needed to identify the light coin, given a balance with two pans for comparing weights.