Did you solve it? Are you a matcha for these tasty Japanese puzzles?
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.
Solution (a) 31 (b) 24 (c) 23
(a) If the lone glove left behind is red, both octopuses can wear green gloves. If the lone glove left behind is green, both octopuses can wear red gloves.
(b) Imagine the first 16 choices are all of one colour. You will then need 8 of the other.
(c) With 23 gloves, at least 7 are one colour (say red) and at least 8 are the other (say green). If there there exactly 7 red, then both octopuses can wear green. If there are more than 7 red, one can wear red and the other green. (Likewise, if at least 7 are green, and at least 8 are red, we get the same result.)
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The diagram below represents a multiplication in which all but two of the digits have been replaced by stars.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.
Solution
Replace the stars with letters A to J.
H must be 1 since F plus the carry of (D+G) must be 10 or larger. In fact, since the carry of D+E can at most be 1, it must be the case that H = 1, I = 0, and F = 9. We also know thanks to the given 1, that D + G = 11. Also, note that E = J
Now to the multiplications. We know that 2 × AB = FG = ninety-somthing. So A = 4. And since C x AB = DE, we can deduce that C is 1 or 2. (If it was 3 or larger C x AB would have threedigits.)
Suppose C = 1. Then AB = DE, which means that D = A = 4. However, we know G must be even, since G = 2 x B, so D + G is even, but this contradicts D + G = 11. Hence C = 2 and D = F = 9. It follows that J = E = G = 2 and B = 6.
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.
Solution
Here's the 4 x 6 and the 3 x 9
And here's the 5 x 6
I hope you enjoyed these puzzles. I'll be back in two weeks. Arigato!
Tasty Japanese Morsels in Recreational Mathematics is 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.
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