An experiment consists of eight steps - H, J, K, L, M, O, P, and S - that all must be performed. Three days are allotted for the experiment. Each step requires exactly one morning or else one afternoon to be performed, and at most two steps can be performed during any given morning or afternoon. The following restrictions must be observed: J must be performed on the second day. P must be performed in the morning. K and M must be performed at the same time. J must be performed at some time after M has been completed and at some time after O has been completed. O must be completed at some time before P and at some time before S. If the experiment is to be completed by the end of the second day, which of the following must be performed on the second day?
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Explanation: Total: 8 steps over 2 days (Day 1: 4 slots, Day 2: 4 slots). Steps: H, J, K, L, M, O, P, S. Constraints: J on Day 2. P in Morning. K and M simultaneous (2 slots). M, O before J. O before P (Morning) and S. M and O before J (Day 2) means M and O must be on Day 1 or Day 2 before J. K and M (2 slots) before J must be Day 1. O before J (Day 2) must be Day 1. Day 1 (4 slots) must contain K, M, O (3 slots). The remaining slot is H or L or P. O must be before P (Morning) and S. If P must be in the morning, and O is on Day 1, P could be Day 2 Morning. If P is Day 2 Morning, J (Day 2) must be Day 2 Afternoon (since J is after P and M and O). If J is Day 2 Afternoon, Day 2 slots used: P (Morning), J (Afternoon). 2 slots remain on Day 2. S must be after O (Day 1). S can be Day 2. Since 3 tasks (K, M, O) are mandatory for Day 1, and only 4 slots are available, there is one remaining slot for H, L, or P. S must be performed on Day 2 (as Day 1 is full). Therefore, S must be performed on the second day. S is the task that must be performed on the second day.