Big thanks to Allen Ball spontaneous problem writer!!!!!

Squeezed Together

This is a hands-on problem. You have one minute to determine which team members will solve the problem.

JUDGE READS TO TEAM (after participants are determined):

You will have 7 minutes to complete this problem. You may talk or ask questions at any time; however, time continues. At the end of 7 minutes, your solution will be scored.

Your problem is to place as many ping pong balls and tennis balls as possible in the square in front of you. You will be given materials to be used in your solution. No other materials may be used.

Each ball must be placed one at a time into the square. The ball must be completely within the taped off area to count for score. Balls that extend past the outside edge of the taped boundary will receive no score. After a ball is placed, a team member must say "done" for that ball before another ball may be placed. Ball may be removed after placement, but they must also be removed one at a time.

Score will be as follows:

Each ping pong ball completely within the square will receive 2 points

Each tennis ball inside the square will receive 4 points

If every tennis and ping pong ball are completely within the square, you will receive 20 additional points.

How well your team works together will receive 1-20 points.

Materials and Setup

Give each team the following materials.

1 sheet of newspaper

1 piece of yarn 12" in length

4 straws

25 toothpicks

A 1" square of clay

5 pieces of spaghetti

1 sheet of construction paper


On a hard surfaced floor or table top, tape off a square for ball placement.

For Division 1, the square will measure 6" x 6"

For Divisions 2 and 3 the square will measure 4" x 4"

Give each team a bag or basket containing 12 ping pong balls and 12 tennis balls. (You may vary this for practice, depending on what you have available, of course). The bag or basket may NOT be used as part of the solution.

The team may use the given materials for containing the balls in the taped area. But be sure they say "done" after a ball is placed, before attempting to place another ball.

When scoring, use a ruler placed on the outside edge of the taped boundary to determine whether a ball is entirely within the boundary. Balls outside the boundary will NOT count for score; however, a ball supported by one outside the boundary WILL count for score if that supported ball is entirely within the square.