Question

This group of questions is based on a set of conditions. In answering some of the questions, it may help to draw a rough diagram. Choose the response that most accurately and completely answers each question.

A circular field, with an inner radius of 10 meters and an 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 following symbols: F1, F2, F3, F4, F5.
2. The points between different stages of the project are referred to by the following 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 it was not given to farmer F1.
7. Farmer F3 was given the work of the stage ending at point P5.

Which stage was ploughed by farmer F5?

• A. First
• B. Second
• C. Third
• D. Fifth

Hint:

Chase the stage-to-point chain from the fixed Stage 3 to P1 clue; F3 ends up with Stage 1, F4 with Stage 4, which leaves Stage 5 as the only stage that starts at P4, matching F5's clue.

Answer 1

The Correct Option is D

Step 1: Fix Stage 3's finish point and locate F3.
Condition 6 fixes Stage 3 as ending at P1. Condition 7 says F3's stage ends at P5, so F3 is not doing Stage 3 (Stage 3 ends at P1, not P5). Condition 4 says the stage running P5 to P3 is not Stage 1; testing Stage 1 as F3's stage works cleanly here, because then Stage 2 (the very next one) becomes the P5-to-P3 stage, which is allowed since Stage 2 is not Stage 1. So F3 ploughs Stage 1, which ends at P5, and Stage 2 runs P5 to P3.

Step 2: Extend the chain to Stage 3 and Stage 4.
Stage 3 starts where Stage 2 ends, at P3, and (from condition 6) finishes at P1, so Stage 3 is P3 to P1. Condition 5 gives Stage 4 to F4, and Stage 4 must start where Stage 3 ends, at P1.

Step 3: Use the F5-starts-at-P4 clue.
Condition 3 says F5's stage starts at point P4. Stage 1 already belongs to F3 (Step 1), so F5 cannot be assigned Stage 1. Working through the remaining stages, Stage 5 is the one left that can start at P4 once Stage 4 is fixed as P1 to P4 (Stage 5 begins exactly where Stage 4 ends). So F5's stage, starting at P4, has to be Stage 5.

Step 4: Confirm there is no other stage F5 could occupy.
Stage 1 is F3's, Stage 4 is F4's, and Stage 2 and Stage 3 are later shown (using condition 6's 'not F1' rule) to belong to F1 and F2 respectively, neither of which starts at P4. Only Stage 5 is left over for F5, consistent with Stage 5 starting at P4 exactly as condition 3 requires.

Final Answer:
Farmer F5 ploughed the Fifth stage. \[ \boxed{\text{Fifth}} \]