The Counterfeit Penny Problem: There are ten stacks of pennies, each with ten pennies. One of the stacks is known to contain all counterfeit pennies. Assume all good pennies weigh the same amount, X. Also assume that all the counterfeit pennies weigh a little less; each weighing the amount, Y. If you're allowed one weighing on a conventional scale, how should you proceed to determine the counterfeit stack?

Answer: Take one penny from the first stack, two pennies from the second stack, three pennies from the third stack, and so on, all the way until all ten pennies from the tenth stack. Weighing these 55 pennies on the scale will reveal how many counterfeit pennies there are, therefore identifying which stack they came from.

N=number of counterfeit pennies (and the numbered stack they came from)

W=actual weight of the 55 pennies

X=weight of good penny

Y=weight of counterfeit penny

N=(W-(55X))/Y