High School Elimination Tournament
Round 1
5th Annual WSMA Math Bowl
March 7th, 2015
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Problem 1
A finite polynomial 𝑓(𝑥) exists such that the
following is true 𝑓(𝑥 − 1) = 𝑓(𝑥 + 1). If
𝑓(7) = 45, what is 𝑓(20)?
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Problem 2
A function 𝑓(𝑥) satisfies the following property :
𝑓(𝑥𝑦) = 𝑓(𝑥 − 𝑦) + 3𝑓(𝑥 + 𝑦). What is 𝑓(4)?
Copyright © 2015 by the Washington Student Math Association
Problem 3
Find the largest integer whose digits sum to 11
and multiply to 24.
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Problem 4
Let a, b, and c be integers such that 𝑎 = 1, and
𝑏, 𝑐 ≥ 1. It is given that 3 𝑎𝑏𝑐
𝑐. What is b?
1
3
≥ 𝑎+𝑏+
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Problem 5
If 11! = 3991𝑎800, what is the value of a?
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Problem 6
I was born on July 3rd, 2000, on Monday. On what
day of the week will I turn 16?
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Problem 7
If 𝑎 = 𝑏 + 3, 𝑏 = 2𝑐, 𝑐 = 𝑑 + 10, 𝑑 = 4𝑒, 𝑒 =
𝑓 + 1, 𝑓 = 3𝑔, what is 𝑔 in terms of 𝑎?
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Extra Question
If r is the radius of the inscribed circle inside a
triangle with side lengths, 3, 4, and 5, what is
the value of r?
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