210hw10 - c, a + b + c is divisible by 3. In other words,...

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Math 210 Homework 10 Due Monday May 2nd 1. For the purposes of this problem, pretend everybody has exactly three names: first, middle, and last. (In real life, some people have no middle name, and some people have more than one middle name, but ignore that.) A crowd of 20,000 spectators are watching a hockey game. Prove that there must be two spectators who have exactly the same initials as each other. 2. (i) If a and b are any two natural numbers, prove that at least one of a, b, a + b is even. (ii) If a , b , c are any three natural numbers, prove that at least one of a, b, c, a + b, b +
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Unformatted text preview: c, a + b + c is divisible by 3. In other words, there must be a string of consecutive num-bers whose sum is divisible by 3. (iii) If a , b , c , d , e , f , g are any seven natural numbers, prove that there must be a string of consecutive numbers in the list whose sum is divisible by 7. 3. (i) The 8 leaders of the G8 countries are standing in a row to have their picture taken. In how many ways can they do this? (ii) In how many ways can they do this if Angela Merkel doesnt want to stand next to Silvio Berlusconi? 1...
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