Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.9 AIME Find the answer

1.1. Five non-negative numbers are written in a row. The sum of any two adjacent numbers does not exceed 1. What is the maximum value that the sum of all five numbers can take?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

1.1. Answer: 3. Example: $1,0,1,0,1$ .

Denoting our numbers as $a, b, c, d, e$ , we get that $a+b+c+d+e=(a+b)+(c+d)+(d+e)-d \leqslant 3$ .

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