Two brothers are scrupulously truthful, with one exception: Each lies about his birthday on his birthday.
On New Year’s Eve you ask what their birthdays are. The first says “Yesterday” and the second says “Tomorrow.”
On New Year’s Day you ask again what their birthdays are. Again the first says “Yesterday” and the second says “Tomorrow.”
What are their birthdays?
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Each brother lies only one day a year, so each must have given at least one truthful response. That means the first brother was born on 12/30 or 12/31 and the second on 1/1 or 1/2. Now, the first brother cannot have been born on 12/30, for that would mean he’d lied unaccountably on New Year’s Day. And the second brother cannot have been born on 1/2, for that would mean he’d lied unaccountably on New Year’s Eve. Thus their true birthdays are 12/31 and 1/1.
From Pierre Berloquin, The Garden of the Sphinx, 1981.
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