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.

Which was the starting point for farmer F3?

• A. P2
• B. P3
• C. P4
• D. P1

Hint:

Clue 7 tells you F3's stage ends at P5. Once the loop of points is fixed using clues 6 and 4, read off the start of the stage that ends at P5.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This question again uses the five-stage circular ploughing puzzle, this time asking for the starting point of farmer F3's stage.

Step 2: Key Formula or Approach:
Build the loop X1 to X2 to X3 to X4 to X5 back to X1 using clues 6 and 4 to fix the points, then use clue 7 directly to find F3's stage.

Step 3: Detailed Explanation:
Clue 6 fixes X4 = P1, since stage 3 finishes at P1.
Clue 4 rules stage 1 out for the "P5 to P3" stage, and testing the remaining slots shows it must be stage 2, so X2 = P5 and X3 = P3.
Only P2 and P4 remain for X1 and X5. Clue 3 ties F5's stage to a start at P4. If X1 were P4, that stage would run P4 to P5, ending at P5, which clue 7 already assigns to F3, a clash. So X1 = P2 and X5 = P4.
The loop becomes: stage 1 = P2 to P5, stage 2 = P5 to P3, stage 3 = P3 to P1, stage 4 = P1 to P4, stage 5 = P4 to P2.
Clue 7 says F3's stage ends at P5. The only stage ending at P5 is stage 1, which runs from P2 to P5. So F3's stage starts at P2.
For completeness, stage 5 starts at P4 so F5 ploughs it (clue 3), F4 ploughs stage 4 (clue 5), and stage 3 is kept away from F1 (clue 6), so F2 ploughs stage 3 and F1 ploughs stage 2.

Step 4: Final Answer:
Farmer F3's stage starts at P2. \[ \boxed{P2} \]