Solution to February’s Puzzle:
Counterfeit Coins
This puzzle is from Clifford Jensen. Suppose you
have 10 stacks of coins, with 10 coins in each
stack. One stack consists of 10 counterfeit coins
and the other 9 stacks each consist of 10 legitimate
coins. Each legitimate coin weighs exactly
1 gram. Each counterfeit coin weighs exactly 0.9
grams. You have a digital scale that’s graduated in
tenths of grams. Using the scale to take only one
reading, determine which stack has the 10 counterfeit
coins. You can weigh any number of coins
from any number of stacks, but must you weigh
them all together (i.e., you can take only one
reading from the scale).
Take 1 coin from stack #1, 2 coins from stack
#2, and so on. Weigh the stack of 55 coins. If all
the coins were legitimate, the scale would show 55
grams. If stack #3 is the stack of counterfeit coins,
the scale will show 54.7 grams because the pile of
coins you weighed contains 3 counterfeit coins and
is therefore 0.3 grams light. More generally, if stack
n is the stack of counterfeit coins and w is the
weight the scale shows, then n = (55.0 - w)/0.1.
March’s Puzzle: Too Clever by Half
A chicken and a half lay an egg and a half in a day
and a half. How many eggs would one chicken lay
in three days? A builder and a half build a house
and a half in a year and a half using a tool and a
half. How many houses would one builder build in
nine years? Can you generalize your calculation to
solve both equations?