## Medium puzzles

In a circle are light bulbs numbered 1 through n, all initially on. At time t, you examine bulb number t, and if it’s on, you change the state of bulb t + 1 (modulo n); i.e., you turn it off if it’s on, and on if it’s off. If bulb t is off, you do nothing. Prove that if you continue around and around the ring in this manner, eventually all the bulbs will again be on.

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Solution
Source: P. Winkler
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There is a 6x8 rectangular chocolate bar made up of small 1x1 bits. We want to break it into the 48 bits. We can break one piece of chocolate horizontally or vertically, but cannot break two pieces together! What is the minimum number of breaks required?

Solution

Assume 100 zombies are walking on a straight line, all moving with the same speed. Some are moving towards left, and some towards right. If a collision occurs between two zombies, they both reverse their direction. Initially all zombies are standing at 1 unit intervals. For every zombie, you can see whether it moves left or right, can you predict the number of collisions?

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Solution
Source: CSEblog
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An infection spreads among the squares of an nXn checkerboard in the following manner. If a square has two or more infected neighbors, it becomes infected itself. (Each square has 4 neighbors only!). Prove that you cannot infect the whole board if you begin with fewer than n infected squares.

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Solution
Source: P. Winkler
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A & B are alternately picking balls from a bag without replacement. The bag has k black balls and 1 red ball. Winner is the one who picks the red ball. Who is more likely to win, the on who starts first, or second?

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Solution
Source: 40 Puzzles
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