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Two couples have babies simultaneously in different hospitals. They don't know the expected gender, and each have one child which is F or M. How can they arrange in advance, given a guess each on birth, that at least one couple will correctly guess the gender of the other's child.

Source: This is based on Ed Felten's Coin toss

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I am interpreting

that each couple can wait to see what gender their own child is before making a guess about the other couple's child. And that "each have one child which is F or M" to exclude twins and intersex.

Then it seems this works:

The first couple guesses that the second couple's baby has the same gender as their own, and the second couple guesses that the first couple's baby has the opposite gender as their own? Exactly one guess will be correct.

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  • $\begingroup$ Damn, guess my guess was wrong. Guess I'll guess again and hopefully my guessing of that guess will be right. $\endgroup$ – a guy Dec 15 '18 at 20:28
  • $\begingroup$ @aguy your guessing of that guess ought to be a better guess, I guess. $\endgroup$ – deep thought Dec 15 '18 at 20:32
  • $\begingroup$ You guess I'll guess again, so I'll guess a guess again. $\endgroup$ – a guy Dec 15 '18 at 20:33
  • $\begingroup$ I like that your answer 'exactly one guess will be correct' is more specific than the question. $\endgroup$ – Tom Dec 15 '18 at 20:40
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The answer is

impossible!

because

There is two genders so no matter what a couple picks there will always be a chance that the baby was of the opposite gender.

However, if we assume that the second guesser gets to know if the first couple was correct or not:

The first guesser can guess by saying what their baby's gender is. If they had the same gender, the second person doesn't need to guess and the first guesser got it correct. However, if they are wrong, the second couple knows that they had opposite genders so can therefore guess the opposite of their baby's gender.

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  • $\begingroup$ You're on the right track. If the first couple guesses right, then it doesn't matter what the second couple guesses (the goal is that at least one guess is right, so they've already "won" if the first couples guessed right. So the second couple might as well assume the first couple guess incorrectly, since that's the only situation where the second couple's guess matters. $\endgroup$ – Acccumulation Dec 17 '18 at 22:57

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