# Collection of puzzles on proper divisors

Make the equation below true by replacing each letter with a unique digit (0-9).

$$P + P + P = I = G + G$$Here's the solution:

\(P + P + P = I,\) and \(I = G + G.\) Thus, \(I\) must be divisible by 3 and 2. The only single digit number with this property is 6, so \(I = 6.\) Now we have \(P + P + P = 6 = G + G,\) so \(P\) is one-third of \(6,\) and \(G\) is one-half. So \(P = 2\) and \(G = 3.\) In conclusion, the equation is \(2 + 2 + 2 = 6 = 3 + 3.\)