# The King's Routes Problem: How many possibilities? [closed]

On a chessboard, a king is to be allowed to move one square at a time: horizontally to the right, vertically downward, or diagonally to the right and downward. Imagine a reduced 4x4 chessboard, with the king beginning in the top-left square. By how many routes can he reach the bottom-right square? By how many routes can a similar journey be made on a full 8x8 chessboard?

## closed as off-topic by elias, Glorfindel, TheGreatEscaper, Ankoganit, Beastly GerbilJan 29 '17 at 13:51

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – elias, Glorfindel, TheGreatEscaper, Ankoganit, Beastly Gerbil
If this question can be reworded to fit the rules in the help center, please edit the question.

• VTC: This is a typical combinatorics textbook problem, not a puzzle. – elias Jan 29 '17 at 10:05
• As a starter puzzle for those less familiar with puzzling, I think it has merit. Textbook problems are a way for beginners to get into puzzling. – Rory Alsop Jan 29 '17 at 12:13