Problem of the Week 965

Ten Four-Letter Words

Using the letters A and B one can form ten four-letter words, if we exclude those having three consecutive letters the same. How many ways are there to place the letters A and B in the spaces of a 4 x 4 grid so that the 4 rows reading left to right, the 4 columns reading top to bottom, and the two diagonals (reading down) consist of the ten words specified.

Source: P98 in the just-released book The Inquisitive Problem Solver by Paul Vaderlind, Richard Guy, and Loren Larson. This book, just published by the MAA http://www.maa.org, is an unusual collaboration between two well-known North American problemists and one Swedish one. The book is mainly a translation of a Swedish problem book, but with much additional material, and has many original and innovative problems.