[Mathematical logic (miscellaneous).] [Tournaments and tournament tables]

In a race of six athletes, Andrey fell behind Boris and two other athletes. Viktor finished after Dmitry but before Gennadiy. Dmitry outpaced Boris but still came after Yevgeny. What place did each athlete take?

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Let's renumber the conditions.

1) Andrey fell behind Boris and two other athletes.
2) Viktor finished after Dmitry but before Gennady.
3) Dmitry outpaced Boris but still came after Yevgeny.

From 1) it follows that Andrey took fourth place, and Boris was one of the first three. From 3) it follows that Dmitry finished ahead of Boris but after Yevgeny. Thus, the first four are determined: Yevgeny, Dmitry, Boris, Andrey.

From 2) it follows that Viktor was ahead of Gennady.

## Answer

The athletes finished in the following order: Yevgeny, Dmitry, Boris, Andrey, Viktor, Gennady. Send a comment

![](https://cdn.mathpix.com/cropped/2024_05_06_c33e2e8ade684f1ef192g-17.jpg?height=360&width=492&top_left_y=0&top_left_x=789)

## Solution

When the divisor is multiplied by 8, a two-digit number is obtained. This means that the divisor does not exceed 12, since \(13 \times 8 = 104\) is a three-digit number. If the divisor is multiplied by the first or last digit of the quotient (which is greater than 8), a three-digit number is obtained, so the divisor is 12. Therefore, \(12 \times 989 = 11868\).

## Answer

\(11868 \div 12 = 989\).