Suppose you have a 10×10 chessboard and 10 tiles comprising the letters of MATHSBOMBE.

First place the M on one of the black squares on the top row. Now arrange the remaining tiles so that each letter appears on the next row on a black square diagonally below the preceding tile. One possible arrangement is illustrated below. What is the total number of different ways of arranging the tiles so that they spell out MATHSBOMBE?

(The two M tiles and the two B tiles are both considered to be the same. The arrangement illustrated below counts as just one possibility; interchanging the Ms or interchanging the Bs do not give rise to different arrangements.)

(If you think that there are 4,321 different ways of arranging the tiles then you should enter 4321.)

Mathsbombe Competition 2017 is organised by the The Department of Mathematics at The University of Manchester.
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