# Before and after

I present you a solitary riddle that became very popular in Europe many years ago. It is a riddle of English origin that was invented a sailor who spent forty years of his life in Sailor's Snug Harboron the island of Staten and that he boasted of having sailed with Captain Randall himself, entertaining visitors with this game, with which, as he said he drew some "extra silver". Over time the game ended up arriving in London, where it became very famous under the name of "The Riddle of Sixteen."

The riddle consists of transpose the black and white pieces in the least possible number of movements. We can move the tile to an adjacent square, if it is empty, or we can jump over an adjacent piece to land in the square next to it, (as long as it is empty). We cannot move diagonally. only within the same row or column (as the tower in chess).

According to an eyewitness, the old sailor was very proud of his skill in the game and when they bought the game he gave a trick to move the pieces in the least number of movements. The poor man was wrong or he may have lost himself in the hole of the lost arts or perhaps the world has advanced since then. The fact is that the methods that describe the books of English riddles and the books on mathematics are defective and can be diminished in several movements.

#### Solution

We show you the solution in 48 movements. On the image board, the boxes have been named with upper or lower case letters and the central box with the asterisk. Since there is only one hole in the board, the movement is trivial knowing the box that contains the piece to move, thus, moving the pieces of the boxes of the following list, in the order indicated, we will be able to transpose all the pieces in only 48 movements.

 h H ∗ F F AND H G ∗ c b h g d F F C ∗ h H B TO C ∗ c to b h H ∗ c F F D G H B C ∗ g h and F F ∗ h H ∗

It seems that there is a solution in only 46 movements discovered by H. E. Dudeney. Are you able to find it?