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 was the finish point for farmer F2?

• A. P1
• B. P2
• C. P3
• D. P4

Hint:

Chain the stages forward from the fixed Stage 3 to P1 clue and the F3 ends-at-P5 clue, which pins Stage 1 to F3 and Stage 3 (ending at P1) to F2, since condition 6 rules F1 out of Stage 3.

Answer 1

The Correct Option is A

Step 1: Fix Stage 3's end point.
Label the five stages in their fixed geometric order around the circle as Stage 1, Stage 2, Stage 3, Stage 4, Stage 5, running one into the next. Condition 6 tells us Stage 3 finishes at P1, so the boundary right after Stage 3 is P1.

Step 2: Combine the F3 and 'P5 to P3' clues.
Condition 7 says F3's stage ends at P5. Condition 4 says the stage running from P5 to P3 is not Stage 1. Trying Stage 3 for this P5-to-P3 role fails, because Stage 3 already ends at P1 (Step 1), not P3. The only other stage that can consistently start at P5 and end at P3 without breaking condition 4 is Stage 2, which forces F3's stage (the one ending at P5) to be Stage 1. So Stage 1 ends at P5, and Stage 2 runs P5 to P3.

Step 3: Chain the points forward to Stage 3.
Since each stage starts exactly where the previous one ends, Stage 3 must start at P3 (where Stage 2 ended), and Step 1 already fixed Stage 3's end at P1. So Stage 3 runs from P3 to P1.

Step 4: Place F5, and hence Stage 4 and Stage 5.
Condition 3 says F5's stage starts at P4. Stage 1 already belongs to F3 (Step 2), so F5 cannot be doing Stage 1; the only stage left that F5 could reasonably start at P4 for is Stage 5. So Stage 5 starts at P4. Condition 5 gives Stage 4 to F4, and since Stage 4 must start where Stage 3 ends (P1) and finish where Stage 5 starts (P4), Stage 4 runs from P1 to P4, and Stage 5 runs from P4 back to Stage 1's starting point, which by elimination is the one remaining label, P2.

Step 5: Assign the two leftover farmers, F1 and F2, to Stage 2 and Stage 3.
Only Stage 2 (P5 to P3) and Stage 3 (P3 to P1) are left unassigned, for F1 and F2. Condition 6 explicitly says Stage 3's work was NOT given to F1, so F1 must be doing Stage 2, which leaves F2 with Stage 3.

Step 6: Read off F2's finish point.
F2 ploughs Stage 3, which Steps 1 and 3 fixed as running from P3 to P1, so F2's stage finishes at P1.

Final Answer:
F2's finish point was P1. \[ \boxed{P1} \]