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2007 Cyprus MO/Lyceum/Problem 16

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Problem

The full time score of a football match was 3-2. How many possible half time results can we have for this match?

\mathrm{(A) \ } 5\qquad \mathrm{(B) \ } 6\qquad \mathrm{(C) \ } 10\qquad \mathrm{(D) \ } 11\qquad \mathrm{(E) \ } 12

Solution

The score can be any combination of x,\ y, 0 \le x \le 3,\ 0 \le y \le 2. There are 4 values for x, 3 for y, so 3 \cdot 4 = 12 \Longrightarrow \mathrm{E}.

See also

2007 Cyprus MO, Lyceum (Problems)
Preceded by
Problem 15
Followed by
Problem 17
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Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams?
Check out Art of Problem Solving's Introduction to Algebra by Richard Rusczyk.
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