How mathematicians think about the puzzle that Christopher Monckton launched in 1999. In 1999 Christopher Monckton launched a new type of puzzle, similar to a jigsaw but with 209 plain green plastic pieces with geometric shapes. To attract interest, and increase sales, he offered a £1,000,000 prize for the first solution if found within a time limit of a few years. I'll describe some of the ideas Alex Selby and I developed to work on this puzzle, and try to explain (without details!) how mathematicians think about such things. I'll also outline where the inventor, who expected the puzzle to be much too hard to be solved, went wrong.