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Difficulty: MediumAnalytical Puzzles and Grouping

Five professional athletes (M, N, O, P, and Q) are assigned to five adjacent lockers, numbered 1 to 5 from left to right. Each athlete plays a different sport (Boxing, Golf, Rugby, Soccer, or Tennis) and is sponsored by a different brand (Alpha, Beta, Gamma, Delta, or Epsilon). The following conditions apply to their locker assignments:

1. The Rugby player's locker is immediately to the left of the Golf player's locker.
2. M's locker is immediately to the right of the locker belonging to the athlete sponsored by Gamma.
3. N plays Tennis and is assigned Locker 3.
4. The athlete sponsored by Delta is assigned a locker at one of the extreme ends.
5. Q's locker is positioned somewhere to the left of O's locker.
6. The Soccer player is sponsored by Beta, and this locker is immediately to the right of N's locker.
7. P plays Boxing.
8. N is not sponsored by Alpha.

Based on the rules provided, which of the following correctly identifies the athlete assigned to Locker 2, along with their sport and sponsor?

  1. M, Golf, AlphaAnswer
  2. B
    O, Soccer, Beta
  3. C
    M, Golf, Epsilon
  4. D
    Q, Rugby, Gamma

Answer

The athlete assigned to Locker 2 is M, who plays Golf and is sponsored by Alpha.
By mapping all rules to a 5-position grid, Locker 1 holds Q/Rugby/Gamma, Locker 2 holds M/Golf/Alpha, Locker 3 holds N/Tennis/Epsilon, Locker 4 holds O/Soccer/Beta, and Locker 5 holds P/Boxing/Delta. The required combination for Locker 2 is therefore M, Golf, and Alpha.

Step-by-Step Solution

1
Place known exact positions.
Locker 3 is N (Tennis).
Directly stated in Rule 3.
2
Use relative positioning clues anchored to knowns.
Locker 4 is the Soccer player sponsored by Beta.
Rule 6 states the Soccer player (Beta) is immediately to the right of N (Locker 3).
3
Deduce remaining sports based on adjacent pair constraints.
Locker 1 is Rugby, Locker 2 is Golf, and Locker 5 is Boxing.
Rule 1 requires Rugby and Golf to be adjacent in that order. The only adjacent empty sport slots are 1 and 2. Therefore, Locker 1 = Rugby, Locker 2 = Golf. By elimination, Locker 5 must be the final sport, Boxing.
4
Assign remaining athletes based on sports and relative clues.
Locker 5 is P, Locker 1 is Q, Locker 4 is O, and Locker 2 is M.
Rule 7 states P plays Boxing, so P is Locker 5. Rule 5 states Q is left of O. The empty athlete slots are 1 and 4, so Q is Locker 1 and O is Locker 4. This leaves Locker 2 for M.
5
Assign sponsors based on positional constraints.
Locker 1 is Gamma, Locker 5 is Delta.
Rule 2 states M (Locker 2) is immediately right of Gamma. Thus, Gamma is Locker 1. Rule 4 places Delta at an extreme end. Since Locker 1 is Gamma, Delta must be Locker 5.
6
Finalize remaining sponsors using negations.
Locker 3 is Epsilon, Locker 2 is Alpha.
The remaining sponsors are Alpha and Epsilon for N (Locker 3) and M (Locker 2). Rule 8 states N is not Alpha, so N is assigned Epsilon. M is assigned Alpha.

Key Concept

Logical Deduction with Multiple Constraints and Spatial Ordering

Alternative Method

You can solve this efficiently by first ignoring the athletes and sponsors and purely solving the sports timeline: N is Tennis at 3; Soccer is right of N at 4; Rugby is left of Golf which must fit into 1 and 2; leaving Boxing for 5. Once the sports are locked in, tying the athletes and sponsors to the sports is straightforward.
Estimated Time:2m 0s
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Topics

Analytical Puzzles and Grouping

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