## Problem of the Month

### Sorting by Reversals

Go get a deck of playing cards. Take ten of the cards: one of each rank from Ace through 10. (Suits don't matter.) Arrange the cards in a row, in the following order:

6 3 7 9 A 4 10 8 2 5

Your goal is to put the cards in ascending order, with the Ace on the left, then the 2, then the 3, and so on up to 10. To get there, you are only allowed to make moves of the following type: pick two cards X and Y, then reverse the order of all the cards in the row from the X to the Y.

For instance, you could start by reversing the cards from the 9 to the 2, producing the following:

6 3 7 2 8 10 4 A 9 5

You could then reverse the cards from the 8 to the 10, which would just exchange those two cards:

6 3 7 2 10 8 4 A 9 5

And so on.

What's the fewest number of moves you would need to put the cards in ascending order, from Ace to 10?

Send your answers to this puzzle to me (Joseph DiMuro) at joseph.dimuro@biola.edu by November 30th, 2014.

## Why Choose Mathematics at Biola?

- Thorough in both educational quality and personal attention to students
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- Involvement in the Putnam Exam; a nationwide contest for math students
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