## Stairways to Heaven

An archaeologist found a Mayan temple shaped like a hexagonal pyramid with four levels. Each of the six sides had four staircases leading from level to level all the way to the top. The number of steps in the staircases varies, so the archaeologist sent four assistants to count them. The first assistant counted the steps in each of the six staircases leading to the level one, the second counted the steps in the six staircases leading from level one to level two, and so on, and they produced the following report:

Ground to Level I:53,50,37,39,42,51.Level I to Level II:37,21,30,25,25,35.Level II to Level III:29,23,17,19,11,17.Level III to Level IV:11,5,7,3,4,9.The archaeologist recorded the numbers on four hexagonal pieces of paper and pinned them at the center to form the model shown below. He realized that although all the assistants visited the staircases in clockwise order, they did not all start from the same side. The total number of steps altogether is 600, so the archaeologist thought that there must be 100 steps on each side.

Rotate the levels so that as many of the six sides as possible have exactly 100 steps.

Ground to Level I:53,50,37,39,42,51.Level I to Level II:37,21,30,25,25,35.Level II to Level III:29,23,17,19,11,17.Level III to Level IV:11,5,7,3,4,9.The archaeologist recorded the numbers on four hexagonal pieces of paper and pinned them at the center to form the model shown below. He realized that although all the assistants visited the staircases in clockwise order, they did not all start from the same side. The total number of steps altogether is 600, so the archaeologist thought that there must be 100 steps on each side.

Rotate the levels so that as many of the six sides as possible have exactly 100 steps.

An old puzzle revived by RGee Watkins, Hemet, California.