# Task № 4.1

## Condition:

Fifth-graders Olya, Fyodor, Katya, and Dima participated in a school olympiad. Out of 8 problems offered at the olympiad, each of the students solved more than four. It is known that:

- Olya solved more problems than Katya,
- Fyodor and Dima solved the same number of problems,
- Dima solved one problem fewer than Olya.

How many problems did each solve if together all four solved 27 problems?

## Answers:

Olya - 8

Fyodor - 7

Katya - 5

Dima - 7

## Exact match of the answer - 1 point

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# Solution.

If the boys solved 5 problems each, then Olya solved 6 problems, and Katya solved 27-5-5-6=11 problems, which cannot be.

If the boys solved 6 problems each, then Olya solved 7 problems, and Katya solved 27-6-6-7=8 problems, which cannot be, because Katya solved fewer problems than Olya.

If the boys solved 7 problems each, then Olya solved 8 problems, and Katya solved $27-7-7-8=5$ problems. This option satisfies the conditions.

The boys cannot solve 8 problems each, as Olya would not be able to solve one more problem.

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