## Medium puzzles

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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A postman brought N letters to a house with two letter-boxes. Since the two boxes were empty, he puts 1 mail in each of the two mail boxes. Then he chooses one of boxes with probability proportional to number of letters present in that box, and puts the 3rd letter in it. He does this for all subsequent letters. What is the expected number of letters in the box with lower letters?

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Solution
Source: P. Winkler
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You have an opportunity to make one bid on an object, whose value to its owner is, as far as you know, uniformly random integer between \$0 and \$100. What you do know is that you are so much better at operating the widget than he is, that its value to you is 80% greater than its value to him. If you offer more than the widget is worth to the owner, he will sell it. But you get only one shot. How much should you bid? For example, if its actual value is \$10, you bid & win at \$11, and sell it for \$18, making profit. But if you bid more than \$18, you make lose! But since u don't know how much its actual price is, how do u bid in order to make some profit?

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Solution
Source: P. Winkler
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