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A toy train produces 10 different tunes when it moves around a circular track of radius 5 meters, at 10 meters per minute.However the toy train is defective and it now produces only two different tunes at random. What is the probability that the toy train produces 6 consecutive music of the same type (1 in ----)? 64, 6, 36, 32

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The difference between the ages of my two granchildren are 3. My eldest grandchild is 3 times older than my youngest grand child and my eldest grandchild's age is 2 more than the ages of my other two grand children added together. What is the age of my youngest grandchild? 51 people (a1,a2,......,a51) meet and shake hands in a circular fashion. In other words, there are totally 51 handshakes involving the pairs (a1, a2),(a2,a3),......,(a50,a51),(a51,a1). Then the size of the smallest set of people such that the rest have shaken hands with at least one person in the set is