MathMania 2007
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In a certain motel, if two students share each room, then two
students will be left without a room. If three students share each
room, then two rooms will be left empty. How many rooms are in the
motel?
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A car went up a hill at an average speed of 30 mph and went down
the hill at an average speed of 60 mph. What was the average speed for
the entire trip?
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What is the angle (in degrees) between the minute hand and hour
hand of a clock that reads 6:20?
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Find the next term in the sequence: 1, 4, 13, 31, 61, 106,...
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What are the last two digits in the decimal expansion of
20072007 ?
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What is the smallest positive integer that is not a divisor of
90! = 90×89×...×3×2×1?
Tiebreaker
How many (decimal) digits are there in
2007! = 2007×2006×...×3×2×1?
(after it is expanded out)? The team getting closest to the correct
answer wins.
Here are the answers.