The Science Quiz: Mathematical puzzles

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Visual: Name the game whose starting setup is shown here. The point is to move the entire stack of disks to another pole, one at a time, but at no point allowing a larger disk to sit atop a smaller one.

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Pick a positive integer. If it’s odd, multiply by 3 and add 1 (so 5 becomes 16). If it’s even, divide by 2 (so 6 becomes 3). Repeat the process with the number you have. The Collatz conjecture is that if you repeat this process enough, you’ll eventually reach X. What’s the value of X?

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When Leonhard Euler solved the problem called the Seven Bridges of Y in 1736, he founded modern graph theory. The idea is to traverse Y, a city, such that one would cross each of its seven bridges only once. Name Y.

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What’s the following problem called? Say you’re on a game show. The host asks you to pick one of three boxes to open. One box has jewels, the other two have nothing. You pick box 1. But instead of opening it, the host opens box 3 and shows you it’s empty. Now, do you pick box 2 or stay with box 1?

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Say you have a _____ ______: a square grid of numbers such that every row and every column sums up to the same value. One unsolved problem asks whether it’s possible to make a 3×3 _____ ______ composed of nine distinct perfect square numbers (e.g. 9, 16, 25, etc.). Fill in the blanks (both pairs have the same words).

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 If you need to place P number of queens on an 8×8 chessboard such that no queen is a direct threat to another, then there are Q number of ways to do it. If Q = 724, then P = 10. If Q = 92, then P = ?