Table of Contents / Nội Dung Chính

**QUESTION**

In a certain game there are 8 steps, referred to as step 1, step 2, and so on with the final step being step 8. The steps are played one after the other. In each step a score of 1, 2, 3, 4, or 5 is obtained. Andrea played the game, getting at least one score of each of 1, 2, 3, 4, and 5, and never getting the same score in consecutive steps. What is the greatest possible score that Andrea could have gotten?

**ANSWER SELECTION**

(A) 28

(B) 29

**(C) 30 (THIS IS CORRECT!)**

(D) 36

(E) 40

**ANSWER EXPLANATION**

To maximize the score, we want to maximize the number of steps where a score of 5 was obtained. Let’s alternate the score of 5 with a score other than 5, each time the other score being a different number from among the scores 1, 2, 3, and 4. Since there are 8 steps, we will be able to maximize the number of steps where a 5 was obtained and also have at least one score of each of the scores 1, 2, 3, 4, and 5.

This is a sequence of scores for steps 1 through 8, respectively, which will lead to the greatest possible score.

The greatest possible score that Andrea could have obtained is 5 + 4 + 5 + 3 + 5 + 2 + 5 + 1 = 30. (C) is correct.

**Clever Academy**

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