3. (7 points) The knightly tournament lasts exactly 7 days. By the end of the fourth day, Sir Lancelot had not yet faced one quarter of the total number of participants. And by this time, Sir Tristan had fought exactly one seventh of the knights that Sir Lancelot had faced. What is the minimum number of knights that could have participated in the tournament?
Answer: 20.

Solution. Let Lancelot not have fought with $x$ knights. Then the total number of knights is $4 x$, and Lancelot fought with $3 x-1$ knights (the total number minus $x$ and Lancelot himself). Then Tristan fought with $\frac{3 x-1}{7}$ knights. To find the smallest possible number of knights, we need to find the smallest $x$ such that $3 x-1$ is divisible by 7. The values $x=1,2,3,4$ do not work, but $x=5$ does. Thus, the smallest possible number of knights is 20.

Criteria. Any correct solution: 7 points.

For the absence of justification that there could indeed be exactly 20 knights, points are not deducted.

Only the correct answer is provided: 2 points.