How many squares fit in bigger square

Your new Fun with Math author has come up with a relatively simple puzzle to start the 2009-10 school year. But, it will take some concentration to figure out the correct answers.

This year, Young Saint Louis.com has put its math contest feature in the hands of George Yu, who is a senior at Francis Howell High School in St. Charles County.

He is the first student to create a math puzzler contest for YSL.com. He follows Ms. Amy Ruzicka, a South County middle school math teacher who created the Math Mania feature for several years.

(For a more in-depth look at George's math life, go to Past Stories icon at the top of the home page and click onto the September, 2009, issue for the introductory story about George and his math background.)

George's first math puzzler involves a 4x5 square which is divided into a grid of smaller 1x1 squares. He's asking you to tell how many different-sized squares can fit inside the 4 x 5 square.

It's important to remember that in counting the number of possibilities posed by the second question, these smaller squares of each size can overlap each other when figuring out how many will fit.

Also, if you plan to enter other Fun with Math contests later this school year, be sure to save this puzzle and the answers (to be given in the November, 2009, edition). George plans to pose a more complicated version of this "squares-within-square" puzzle in a future contest.

The Fun with Math contest will be run with the same rules and conditions that governed last year's Math Mania contest. They are:

1. Print out the following entry form.
2. Fill out your name, address and telephone number. (Print clearly please)
3. Include the name of your school and math teacher.
4. Answer the puzzle questions for October.
5. Put your completed entry into a stamped, addressed envelope.
6. Be sure to print the entry form so we can be sure of spelling.
7. Mail the entry to: