5040

5040 is a game consisting of seven hexagons, each of which has its six edges marked by the numbers 1 to 6 in some order. To win, match all the numbers! There are 7 pieces with 6 orientations. This gives 7!·6^7 ways. The puzzle as a whole has six orientations that are considered identical, so there really only 7!·6^6=235,146,240 ways of putting the pieces back into its box. As is so often the case with puzzles like this, that number is not really representative of its difficulty. The orientations are all forced because each newly placed piece has to match at least one other, so there are certainly no more than 7!=5040 positions to check when solving it. In fact most of these positions fail to match its colours well before you place the seventh piece, the actual number is far less. If you are fast enough and with only a few movements, you can get the 5040 score!