Puzzle 5 - Tower of Pies

Puzzle: Mr. Frezzo hands out this puzzle, on paper.

Jason’s Catering Service happens to be the best in the world when it comes to pies. His quality service is precise and always exceeds the expectations of his customers. How does he do it?

Let’s use this one particular job as an example. One of Jason’s loyal customers, Mr. Chase, just happened to order 4 different types of pie on Monday, one of each type. What makes Jason’s service so special is that he stacks the pies in the exact same fashion on his delivery truck as he does in his warehouse.

Due to the delicateness of Jason’s gourmet pies, they must be kept at or very near a specific temperature, depending on the type of pie (marked in degrees Fahrenheit). Jason has designed special pie-specific trays to maintain these temperatures. However, by the nature of these high-technology trays, a ‘colder’ pie can never be placed below a ‘hotter’ pie. For example, in the course of all Jason’s moves, Apple can never be below Strawberry or Huckleberry.

He can only move one type of pie at a time, and he has a special pre-loading point to help keep everything in order. By moving a pie from one place to another, that counts as one move. In the end, his delivery truck has the pies stacked in the same way as they were at the warehouse, as expected from such a dedicated service.

Now, what is the minimum number of moves, represented by X, it takes to move 31 different types of pie, one of each, from his warehouse to the delivery truck?

When you finish, go to www.twitter.com/_X for the next stage!

[Solution: This puzzle is pretty simple; it’s just the Tower of Hanoi! The solution leads students to the Twitter account @_2147483647 for the next puzzle.]

Hint 1: Try 1 pie. Then 2. Then 3. Then… wait a minute…

Hint 2: Credits to Mr. Lucas for providing the pies!

Hint 3: Mr. Mersenne deals with all of the logistics.