Stockton took the National Math test at the beginning of this month. They were able to bring the booklet of questions home. Some of the questions are so crazy, and pretty funny. For example:
Eight people are sitting around a circular table, each holding a fair coin. All eight people flip their coins and those who flip heads stand while those who flip tails remain seated. What is the probability that no two adjacent people will stand?
Claudia has 12 coins, each of which is a 5-cent coin or a 10-cent coin. There are exactly 17 different values that can be obtained as combinations of one or more of her coins. How many 10-cent coins does Claudia have?
Hexadecimal (base-16) numbers are written using the numeric digits 0 through 9 as well as the letters A through F to represent 10 through 15. Among the first 1000 positive integers, there are n whose hexadecimal representation contains only numeric digits. What is the sum of the digits of n?
Needless to say, I'm glad I wasn't the one taking this test!
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