## MindCipher

### May 10, 2013

According to their masthead, the MindCipher website is “a social repository of the world’s greatest brain teasers, logic puzzles and mental challenges.” Some of the problems lend themselves to brute force computation, others are better solved with pencil-and-paper or solely with mental effort. We look at three MindCipher exercises today.

1: Coin Flip: On Monday, you flip a coin all day. You start flipping it until you see the pattern Head, Tail, Head. You record the number of flips required to reach this pattern, and start flipping again (and counting up from 1 again) until you see that pattern again, you record the second number, and start again. At the end of the day you average all of the numbers you’ve recorded. On Tuesday you do the EXACT same thing except you flip until you see the pattern Head, Tail, Tail.

Will Monday’s number be higher than Tuesday’s, equal to Tuesday’s, or lower than Tuesday’s?

2: 1978: The year 1978 is such that the sum of the first two digits and the latter two digits is equal to the middle two digits, i.e. 19 + 78 = 97. What is the next year (after 1978) for which this is true?

3: Sum of Two Prime Numbers: If p, q > 2 are consecutive in set of primes. Since p,q can only be odd number, (p+q) is an even number.

Can (p+q)/2 be prime?

Your task is to solve the three problems given above; write a computer program to help you if you wish. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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