Q: Two octopuses will fight using boxing gloves but they each need 8(!) gloves and the gloves MUST be the same color.
Drawing at random from a bag that has 16 red gloves and 16 green gloves, what is minimum number of gloves to guarantee that the colors of the gloves of the two octopuses are:
(a) the same.
(b) different.
(c) either the same or different.

 A: (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) Ifmagine 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 color (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.)

With many thanks to Alex Bello’s Monday puzzles in the Guardian:
https://www.theguardian.com/science/2025/aug/18/did-you-solve-it-are-you-a-matcha-for-these-tasty-japanese-puzzles