Scheduling Logic Puzzle Solution

This problem requires deducing the day each person plays their game based on a set of constraints for a week (Monday to Sunday).

Step 1: Establish the Weekly Schedule Framework

Create a schedule grid for the week:

Step 2: Apply Direct Clues

• M plays on Wednesday.
• Only two persons play between M and Q. Since M is on Wednesday, Q must be 3 days after Wednesday (Thursday, Friday) or 3 days before Wednesday (Tuesday, Monday). As each plays on a different day, Q must be on Saturday (Wednesday + 3 days).

Updated Schedule:

Step 3: Apply Relative Clues (O and R)

• O plays immediately before R (OR).
• O does not play on Thursday.

Considering the remaining slots (Mon, Tue, Thu, Fri, Sun), the only consecutive days available for O and R where O is not Thursday are Monday and Tuesday. Thus, O plays on Monday and R plays on Tuesday.

Updated Schedule:

Step 4: Apply Remaining Clues (N and S)

• Remaining people: N, P, S.
• Remaining days: Thursday, Friday, Sunday.
• N does not play on Sunday. Therefore, N must play on Thursday or Friday.
• Only two persons play between N and S.

Let's test the placement of N and S:

• If N plays on Thursday (Day 4): To have 2 people between N and S, S must be on Sunday (Day 7). The days between are Friday (Day 5) and Saturday (Day 6). However, Q plays on Saturday. This placement is impossible.
• If N plays on Friday (Day 5): To have 2 people between S and N, S must play on the day 3 slots before Friday. Days are Wed(3) and Thu(4). M plays on Wed. So, S must play on Thursday (Day 4).

Placement based on N=Friday and S=Thursday:

• S = Thursday
• N = Friday

Check N/S constraint: S(Thu) _ _ N(Fri). Requires Wednesday between them. M plays on Wed. This only leaves 1 day (Wed) between S and N, not 2. This deduction path failed.

Let's re-evaluate the N/S constraint combined with the known schedule: O(Mon), R(Tue), M(Wed), _(Thu), _(Fri), Q(Sat), _(Sun).

• Remaining days for N, P, S: Thu, Fri, Sun.
• N cannot be Sun. N is Thu or Fri.
• Consider the pair (N, S) with 2 days between. Possible pairs across the week are (Mon, Thu), (Tue, Fri), (Wed, Sat), (Thu, Sun).
• Check N != Sun:
  • If N=Thu, S=Sun? Pair (Thu, Sun). Days between are Fri, Sat. Sat=Q. Fails.
  • If N=Fri, S=??. Can't be Thu (0 days between). Can't be Sun (1 day between).
  • If S=Thu, N=??. Can't be Fri (0 days between). Can't be Sun (1 day between).
  • If S=Fri, N=??. Can't be Thu (0 days between). Can't be Sun (1 day between).
• Let's test the constraint N _ _ S or S _ _ N with the available slots Thu, Fri, Sun for N,P,S.
  • If N = Thu. Can S = Sun? Days between Thu & Sun are Fri, Sat. Sat = Q. Fails.
  • If N = Fri. Can S = ?? N cannot be Sunday. The remaining days are Thu, Fri, Sun. S could be Thu or Sun. If S = Thu, 0 days between. If S = Sun, 1 day (Sat) between. Fails.
  • If S = Thu. N must be placed. N != Sun. So N=Fri. Days between S(Thu) and N(Fri) = 0. Fails.
  • If S = Fri. N must be placed. N != Sun. So N=Thu. Days between S(Fri) and N(Thu) = 0. Fails.
• There seems to be a misunderstanding. Let's assume P takes one of the remaining slots and place N and S based on the constraint and remaining slots.
• Final available slots: Thu, Fri, Sun. People: N, P, S. N != Sun.
• Try placing N and S:
  • Consider N=Thu. Needs S such that 2 days are between. S=Sun is the only option among remaining days. Days Fri, Sat are between. Sat=Q. Fails.
  • Consider N=Fri. Needs S such that 2 days are between. No remaining slots work.
  • Consider S=Thu. Needs N such that 2 days are between. N=Sun required, but N!=Sun. Fails.
  • Consider S=Fri. Needs N such that 2 days are between. No remaining slots work.
• Let's revisit: O(Mon), R(Tue), M(Wed), _(Thu), _(Fri), Q(Sat), _(Sun). People: N, P, S. N!=Sun.
• If N = Thu: S must be placed on Fri or Sun. P takes the last slot.
  • If S=Sun: (N=Thu, S=Sun). 2 days between (Fri, Sat). Sat=Q. This doesn't work.
  • Wait, maybe N and S don't use the *remaining* days? The only remaining days are Thu, Fri, Sun. N must be Thu or Fri.
  • Let's place N=Thu. Remaining days for P, S are Fri, Sun.
  • If S=Fri, P=Sun. Constraint: 2 days between N(Thu) and S(Fri)? NO.
  • If S=Sun, P=Fri. Constraint: 2 days between N(Thu) and S(Sun)? Days Fri, Sat between. Sat=Q. OK. Check N!=Sun. N=Thu. OK.
  • So, N=Thu, P=Fri, S=Sun.
• Let's verify this configuration:
  • Mon: O
  • Tue: R
  • Wed: M
  • Thu: N
  • Fri: P
  • Sat: Q
  • Sun: S
  Check constraints:
  • M=Wed. YES.
  • 2 between M(Wed) and Q(Sat)? YES (Thu, Fri).
  • O before R? YES (Mon-Tue).
  • O not Thu? YES (O=Mon).
  • 2 between N(Thu) and S(Sun)? YES (Fri, Sat).
  • N not Sun? YES (N=Thu).
  All constraints are satisfied.

Step 5: Determine P's Playing Day

Based on the deduced schedule, P plays the game on Friday.