Question

Directions: A circular field, with inner radius of 10 meters and outer radius of 20 meters, was divided into five successive stages for ploughing. The ploughing of each stage was handed over to a different farmer.

1. Farmers are referred to by the symbols F1, F2, F3, F4, F5.
2. The points between different stages are referred to by the symbols P1, P2, P3, P4, P5, not necessarily in that order.
3. Farmer F5 was given the work of ploughing the stage starting at point P4.
4. The stage from point P5 to point P3 was not the first stage.
5. Farmer F4 was given the work of the fourth stage.
6. Stage 3 finished at point P1, and the work of which was not given to farmer F1.
7. Farmer F3 was given the work of the stage ending at point P5.

For which farmer was P2 a finishing point?

• A. F1
• B. F2
• C. F3
• D. F5

Hint:

Pin down the full loop of points using clues 6 and 4 first, then check which stage starts at P4, since clue 3 ties that stage to farmer F5.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
This question continues the same five-stage circular ploughing puzzle. We must find which farmer's stage finishes at point P2.

Step 2: Key Formula or Approach:
Write the ploughing order as a loop X1 to X2 to X3 to X4 to X5 back to X1, where X1 to X5 is some arrangement of P1 to P5 and stage n goes from Xn to X(n+1). Fix the points using clues 6 and 4 first, then use clues 3, 5, and 7 to assign the farmers.

Step 3: Detailed Explanation:
Clue 6: stage 3 finishes at P1, so X4 = P1.
Clue 4: the "P5 to P3" stage is not stage 1, and it can only sit at stage 2 without clashing with X4 = P1, so X2 = P5 and X3 = P3.
Only P2 and P4 are left, for X1 and X5. Clue 3 says F5's stage starts at P4. If P4 were X1, F5's stage would run P4 to P5, which also ends at P5, but clue 7 already sends the "ends at P5" stage to F3, a clash. So X1 = P2 and X5 = P4.
The loop is now: P2 to P5 (stage 1), P5 to P3 (stage 2), P3 to P1 (stage 3), P1 to P4 (stage 4), P4 to P2 (stage 5).
Stage 5 starts at P4, so by clue 3, farmer F5 ploughs stage 5, which runs from P4 to P2. So the stage that finishes at P2 is stage 5, ploughed by F5.
Checking the rest for completeness: stage 1 ends at P5, so by clue 7, F3 ploughs stage 1. By clue 5, F4 ploughs stage 4. Clue 6 keeps stage 3 away from F1, so F2 ploughs stage 3 and F1 ploughs stage 2.

Step 4: Final Answer:
P2 is the finishing point of stage 5, which was ploughed by farmer F5. \[ \boxed{F5} \]