huinventors1-3, Exercise 3: 43 quintillion and 20

Model answer:

The 43 quintillion figure counts the number of different reachable positions. God's number, 20, is the largest number of moves needed to solve any one of them with the best possible solution. They measure different things. A huge number of positions can still all be close to the solved state, because each move can lead to several new positions, so the number of positions reachable grows very quickly with each move. The number of positions within 20 moves is therefore enough to cover them all. This is why the figures do not conflict. The figures and the counting method should be checked.