Three people at a party discover that the product of any two of their ages is equal to the year in which the third was born.

What is the most recent year the party could have taken place?

It seems that all three partygoers must be 44, and since 44x44 = 1936, this would be the age of the third person in the year 1980.

Consider a situation where the ages are not all the same, say ages of 43, 44, and 45. The [products of these ages is 1892, 1935, and, 1980. Not only do these values not meet the requirements of the puzzle, but subtracting each of those numbers from any given year gives too large a disparity in ages, which when you multiply them together gives products that are even further apart. In other words, it seems the three partygoers must be the same age for this to work.

Posted by Bryan on 2003-07-21 09:49:19