This is another thoughtful puzzle from the imaginative mind of James Tanton (with slight edits).

“Three poles of height 1183 feet, 182 feet, 637 feet stand in the ground. Pick a pole and saw off all the taller poles at that height. Plant those tops in the ground too. Repeat until no more such saw cuts can be made. Despite choices made along the way, what final result is sure to occur? [Four poles, heights a, b, c, d ft?]”

Answer.

See the Pole Leveling Puzzle for a solution.