Saturday Photographer Puzzle II: The Barcelona Barber

This is the right day for this puzzle. My long hair is being sacrificed in a little while for my youngest brother’s wedding tomorrow.

Anyway, enough crying. A Barcelona barber usually gives good hair cuts, but today he was spectacular. Ten in a row, absolutely perfect. He hires a photographer to take pictures of the pleased clients in different arrangements.

The photographer is no dummy. He knows the solution to today’s other puzzle and wants to get home in a reasonable amount of time, so he asks for some constraints.

It’s good with the barber. “Take them in two rows of five each. Let each man be taller than the man to his left, and let each man be taller than the man immediately in front of him. And take all the arrangements like that!”

The photographer agrees. How many photos will he take?

I’ve lost track completely of Bertie Taylor, who first posed this to me. I don’t know his source.