A friend of mine collects gold coins. One day, his wife asks, “How many do we have?” He tells her, “If I divide the coins into two groups, then 33 times the difference between the number of coins in each group equals the difference between the squares of the two numbers.” How many coins do they have?

Solution to the Problem: They have 33 coins. Use algebra to solve: James Alarie and David and Judy Dixon pointed out that any even number of coins will also work, since they could be split into two equal piles. So, I should amend my explanation above. You can only divide by (x - y) as long as (x - y) is not zero! If x - y = 0, then x = y, and the number of coins, x + y = x + x = 2x (which is any even number).

Correctly solved by: