Japan is a world puzzle superpower. Its grid logic puzzles – like Sudoku, Kakuro, KenKen and many more – are played across the world by millions every day.
The country also has its own culture of mathematical puzzles, nurtured by the Academy of Recreational Mathematics, Japan, which was founded in 1979.
Today’s problems are by Yoshiyuki Kotani, a founder member of the Academy and a professor of engineering at Tokyo University. They are taken from his new book, Tasty Japanese Morsels in Recreational Mathematics.
1. Squid game
Two octopuses will face off in a boxing match. Each octopus requires eight gloves. (There is no distinction between left and right gloves.) The rules of octopus boxing stipulate that an octopus must only wear gloves of the same colour.
There is a bag containing 16 red gloves and 16 green gloves. Find the minimum number of gloves that must be drawn at random from the bag to guarantee that the colours of the gloves of the two octopuses are
(a) the same.
(b) different.
(c) either the same or different.
2. Sum-o wrestling.
The diagram below represents a multiplication in which all but two of the digits have been replaced by stars. Reconstruct the computation.
3. Another boxing puzzle
A restaurant uses 4 × 4 and 5 × 5 Bento boxes each divided into exactly eight square sections, as shown in the diagram below
The chef has asked you to create Bento boxes with rectangular boxes. Each Bento must still have eight square sections, even though, as in the example, the square sections do not have to be all of the same size.
Design a 4 × 6 Bento box, a 3 × 9 Bento box, and a 5 × 6 Bento box.
I’ll be back at 5pm UK. PLEASE NO SPOILERS. Please discuss your favourite Japanese things.
Tasty Japanese Morsels in Recreational Mathematics by Yoshiyuki Kotani s published by the American Mathematical Association. All the diagrams above are taken from the book.
I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
PS: Might anyone with computer skills be able to help me create a web page for a puzzle that involves dragging shapes around the screen? I hope to use the puzzle in a future column. If you think you can help, email me.