16 Puzzles for International Puzzle Day

January 29, 2008

Today (Tuesday, January 29) is International Puzzle Day. To celebrate, here are 16 puzzles from the Wolfram Demonstrations Project.

1. Box Packing	2. Dissection Fallacy
Can 27 3×4×5 blocks be placed in a 12×12×12 box? How about 27 a×b×c blocks?	Four identical shapes have an area of 64 or 65, depending on their arrangement. How?
3. Box Toppling Patterns	4. Four-Color Maps
A box gets rolled around on a floor. After 5 topples, how many different places can it be?	What is the connection between borders and map coloring?
5. Shortest Time Problem	6. Loculus of Archimedes
A tennis ball is thrown in a lake. What route allows the ball to be retrieved in the shortest time?	If a square is divided into the above shapes, how many different ways can the square be made?
7. Number of Squares in a Square	8. Measuring the Speed of Light with Marshmallows
How many squares are in this grid of squares?	You have a bag of marshmallows and a microwave. How can you measure the speed of light?
9. The Statue of Regiomontanus	10. Orchard-Planting Problem
Where should you stand so that a statue appears to be as large as possible?	Can 10 trees be arranged so that there are 5 rows, each containing 4 trees?
11. Eight Queens Puzzle	12. Guilloché Patterns
How many ways can 8 queens be placed on a chessboard so that none attack each other?	What are the rules for the strange curves found on paper currency?
13. Lights Out Puzzle	14. Urn Problem
Click on a square to change neighboring lights. How can all the lights be turned off?	An urn holds 7 good balls, and 20 bad balls. If 5 balls are chosen, what are the odds that 2 will be good?
15. The Circle Covering Puzzle	16. Haberdasher’s Problem
Can you completely cover the orange shape with the given set of disks?	Can a square be cut into 4 pieces and rearranged into an equilateral triangle?