1. Final Elimination Tournament
6th Annual WSMA Math Bowl
January 23rd 2016
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Problem 1
What is the smallest perimeter of a rectangle with area 12 and integer side lengths?
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Problem 2
How many different combinations of 4 pencils can you choose from a pile of 3 green pencils, 5 blue pencils and 7 red pencils if the pencils are indistinguishable except for color?
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Problem 3
If 𝑎 2 + 𝑏 2 + 𝑐 2 =1 and 𝑎 3 +𝑏 3 + 𝑐 3 =1, where a, b, and c, are non-negative numbers, then what is the value of 𝑎+𝑏+𝑐?
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Problem 4
If peanuts are sold in packs of 5 or 8, what is the maximum number of peanuts that you cannot buy?
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Problem 5
If 𝑓 𝑥 = 3𝑥 2 +10𝑥+6 and 𝑔 𝑥 = 2𝑥 3 + 7𝑥 2 +4, what is f(g(2))?
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Problem 6
Nine chairs in a row are to be occupied by six students and Professors Sean, Anirudh, and Isabel. These three professors arrive before the six students and decide to choose their chairs so that each professor will be between two students. In how many ways can Professors Sean, Anirudh, and Isabel choose their chairs?
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Problem 7
A cone has a height of 8 and a base circumference of 12pi. What is its surface area in terms of pi?
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Extra Question
A store prices an item in dollars and cents so that when 4% sales tax is added, no rounding is necessary because the result is exactly n dollars where n is a positive integer. What is the smallest value of n?
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