1. The real numbers a 1, a 2, a 3,..., a 20 are written in that order arounda ci

Question

1. The real numbers a1, a2,a3,..., a20 are written in that order arounda circle. Given that a1=a11=2,a14=3, and that the sum of any four consecutive terms is20, find a4. a)12   b)13   c)14  d)15   e)16 2. If there are 6,000,000,001 people in the world and each hasless than 100,000 hairs on hsi or her head, find the maximum numberof people that MUST have the same number of hairs on theirhead. a) 35,445    b)35,456  c)67,435    d)60,001   e) 56,567 1. The real numbers a1, a2,a3,..., a20 are written in that order arounda circle. Given that a1=a11=2,a14=3, and that the sum of any four consecutive terms is20, find a4. a)12   b)13   c)14  d)15   e)16 2. If there are 6,000,000,001 people in the world and each hasless than 100,000 hairs on hsi or her head, find the maximum numberof people that MUST have the same number of hairs on theirhead. a) 35,445    b)35,456  c)67,435    d)60,001   e) 56,567

Explanation / Answer

2. Each of 6,000,000,1 is assigned one of 100,000 numbers. Thepigeonhole principle states that each number of hairs has at least60,000 people assigned to it. But, 6,000,000/100,000 is exactly60,000. So the 1 additional person ensures that there is a numberof hairs that has 60,001 people. Answer: D

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