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# In a certain game there are 8 steps, referred to as step 1,

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In a certain game there are 8 steps, referred to as step 1, [#permalink]  29 Jun 2020, 08:43
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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?

A. 28

B. 29

C. 30

D. 36

E. 40
[Reveal] Spoiler: OA

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Founder
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Kudos [?]: 3014 [0], given: 11279

Re: In a certain game there are 8 steps, referred to as step 1, [#permalink]  29 Jun 2020, 08:43
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Re: In a certain game there are 8 steps, referred to as step 1, [#permalink]  29 Jun 2020, 09:39
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This is really a great question.

We have to think very logically to solve this question.
We want the maximum score, and we want at least one of each 1,2,3,4, and 5. Also, we can't have the same score in consecutive steps.

To maximize the score we have to maximize the score of 5.
The way to do that would be

Step 1 - 5
Step 2 - 4
Step 3 - 5
Step 4 - 3
Step 5 - 5
Step 6 - 2
Step 7 - 5
Step 8 - 1

In this way, each of 1,2,3,4, and 5 is used at least once and we have the maximum no of 5s.

The total score becomes = $$5 \times 4 + 4 + 3 + 2 + 1 = 30$$

OA, C
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Re: In a certain game there are 8 steps, referred to as step 1,   [#permalink] 29 Jun 2020, 09:39
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