Four tasks (A, B, C, D) are scheduled on four days (1, 2, 3, 4), one task per day.
- A is before B.
- C is not on day 1.
- D is on day 3 or 4.
- B is not on day 4.
- Step 1: Check conditions.
D on 3 or 4, so D cannot be on 2.
- Step 2: Verify others.
Arrangement: A, B, D, C. Day 2 = B.
Alternative: A, B, C, D (D on 4).
Day 2 = B or C possible.
A possible if B on 3. D never on 2.
- Step 3: Check options.
Options: (1) A, (2) B, (3) C, (4) D.
D matches option (4).
- Step 4: Conclusion. Option (4) is correct.





For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: