# 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 $$2 + 2 + 2 = 6 = 3 + 3.$$