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2008 AMC 10B Problem 1

Problem 1 of 25EasierCounting & Probability

A basketball player made 55 baskets during a game. Each basket was worth either 22 or 33 points. How many different numbers could represent the total points scored by the player?

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Solution

If kk of the baskets are worth 33 points and the rest worth 2,2, the total is 2(5−k)+3k=10+k.2(5-k)+3k=10+k. As kk ranges over 0,1,…,5,0,1,\ldots,5, the total takes every integer value from 1010 to 15,15, giving 66 possibilities. Thus, the correct answer is E.

More practice

Concepts: basic counting · systematic listing

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.