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Prove, that if you write down the numbers, 1,2,...,101 in an arbitrary order,you can pick 11 numbers that make a monotonous sequence if they are considered in the order they were written down.

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When Arthur is as old as his father Hailey is now, he shall be 5 times as old as his son Clarke is now. By then, Clarke will be 8 times older than Arthur is now. The combined ages of Hailey and Arthur are 100 years. How old is Clarke? In certain community, there are thousand married couples. Two thirds of the husbands who are taller than their wives are also heavier and three quarters of the husbands who are heavier than their wives are also taller. If there are 120 wives who are taller and heavier than their husbands, how many husbands are taller and heavier than their wives?