Biblically Centered Education

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 by November 30th, 2014.

Molly Folkert

I would choose math at Biola is that math is taught as a part of God's creation and my love for math grows alongside my love for God.
-Molly Folkert
Applied Mathematics Major

Naomi Copland

Being a math major has equipped me with deeper knowledge, understanding, and fascination of the subject. Due to this, I feel more excited, confident, and prepared to help future math students succeed in this subject.
-Naomi Copland
Secondary Teaching Mathematics Major

Megan Beatty

I'm so glad I chose to study math at Biola - the faculty incredible and invested in their student’s lives, and I know they care about me in and out of the classroom. It's also been an invaluable opportunity to have consistent integration of my major and my faith and see how God can be glorified through math, which has been one of my favorite aspects of the department.
-Megan Beatty
Pure Mathematics Major

Why Choose Mathematics at Biola?

  • Thorough in both educational quality and personal attention to students
  • Faculty and students work together to make the study of mathematics a successful and enjoyable learning experience
  • Involvement in the Putnam Exam; a nationwide contest for math students
  • Experienced faculty who not only teach classes in which they are specialists, but work on research projects with individual students
  • Small class sizes
  • Readily accessible computing facilities

Biola University
13800 Biola Ave. La Mirada, CA 90639