A survey of participants was conducted at the Olympiad. $50\%$ of the participants liked the first round, $60\%$ of the participants liked the second round, $70\%$ of the participants liked the opening of the Olympiad. It is known that each participant liked either one option or all three. Determine the percentage of participants who rated all three events positively.
1. Let \( a \) be the number of participants who liked only the first round.
2. Let \( b \) be the number of participants who liked only the second round.
3. Let \( c \) be the number of participants who liked only the opening of the Olympiad.
4. Let \( d \) be the number of participants who liked all three events.

Given:
\[
\frac{a+d}{a+b+c+d} = 0.5
\]
\[
\frac{b+d}{a+b+c+d} = 0.6
\]
\[
\frac{c+d}{a+b+c+d} = 0.7
\]

5. Adding these three equations:
\[
\frac{a+d}{a+b+c+d} + \frac{b+d}{a+b+c+d} + \frac{c+d}{a+b+c+d} = 0.5 + 0.6 + 0.7
\]

6. Simplifying the left-hand side:
\[
\frac{a+d + b+d + c+d}{a+b+c+d} = 1.8
\]
\[
\frac{a+b+c+3d}{a+b+c+d} = 1.8
\]

7. Let \( N = a + b + c + d \) be the total number of participants. Then:
\[
\frac{a+b+c+3d}{N} = 1.8
\]

8. Multiplying both sides by \( N \):
\[
a + b + c + 3d = 1.8N
\]

9. We know that \( a + b + c + d = N \). Subtracting this from the previous equation:
\[
(a + b + c + 3d) - (a + b + c + d) = 1.8N - N
\]
\[
2d = 0.8N
\]

10. Solving for \( d \):
\[
d = \frac{0.8N}{2} = 0.4N
\]

11. Therefore, the percentage of participants who rated all three events positively is:
\[
\frac{d}{N} \times 100\% = \frac{0.4N}{N} \times 100\% = 40\%
\]

The final answer is \(\boxed{40\%}\).