How many different ways can you fill the 5 boxes with the digits 1 through 5, using each digit exactly once, so that each number in a shaded box is larger than its two neighbors?
My computer says there are 16 such numbers as follows:
(13254, 14253, 14352, 15243, 15342, 23154, 24153, 24351, 25143, 25341, 34152, 34251, 35142, 35241, 45132, 45231) = 16 such numbers.
