The Pail Problem is a classic problem in computer science. It involves filling a pail with water using two buckets of different sizes. The goal is to measure out a specific amount of water using the two buckets. The solution to the Pail Problem requires finding the right combination of bucket sizes and amounts of water to fill the pail. The crossword solution for the term PAIL PROBLEM is HOLE, which refers to the HOLE in the bottom of the pail that allows the water to be measured out.