A "W" number is one whose digits are initially decreasing, then alternate between decreasing and increasing making exactly three changes of direction. Defining the first and last digit as always being either a peak or a valley, a W number has 3 peaks and 2 valleys.

For example 98246417 is a W number, with peaks at 9, 6, and 7; and valleys at 2 and 1. But 874679642 is not, because it only has 2 peaks and 2 valleys making only two changes of direction.

How many 10-digit pandigital W numbers are there?

The required # 10-digit pandigital W numbers are: 100530.

Posted by K Sengupta on 2023-05-30 22:24:58