Finding A Treasure
A mathematician, before his death, hid a lead-lined, sealed chest containing tens of millions of dollars in gold and jewels in one of two labyrinths, which he then flooded with silt and sea water. He left his only son just enough money to pump out ONE of the two labyrinths. If the son correctly deduced which labyrinth held the chest, he would successfully inherit a fortune. The chest is buried in an interior room with 3 doors.
Labyrinth A has 4 outside doors.
Labyrinth B has 3 outside doors.
Which labyrinth should the son pump out to recover the chest?
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1 solution
Labyrinth B must have an interior room with an odd number of doors. Since each door has two sides, a doorknob on each side, there are 2n doorknobs in total where n is the total number of doors. 3 of these face the exterior, so there are 2n - 3 interior doorknobs. At least 1 room must therefore have an odd number of doors.