Six hockey players: H1, H2, H3, H4, H5 and H6 are sitting in a row facing north (not necessarily in the same order). There are three players between H4 and H2. H4 is not at any of the end. Only three players are between H1 and H5. H3 is towards the left of H6. H1 is at one of the ends. H2 is towards the right of H4. Which of the following statement is NOT correct?
Six hockey players: H1, H2, H3, H4, H5 and H6 are sitting in a row facing north (not necessarily in the same order). There are three players between H4 and H2. H4 is not at any of the end. Only three players are between H1 and H5. H3 is towards the left of H6. H1 is at one of the ends. H2 is towards the right of H4. Which of the following statement is NOT correct?
Solution
Let the six positions be numbered 1 to 6 from left to right.
Given that H1 is at one of the ends, H1 is at position 1 or position 6.
Given that three players are between H1 and H5, they must be at positions (1,5) or (2,6) in some order. Since H1 is at an end:
- If H1 is at position 1, then H5 is at position 5
- If H1 is at position 6, then H5 is at position 2
Given that three players are between H4 and H2, they must be at positions (1,5) or (2,6) in some order.
Given that H4 is not at any end, H4 cannot be at position 1 or 6.
Given that H2 is towards the right of H4.
Combining these: H4 must be at position 2 and H2 must be at position 6.
Since H2 is at position 6, H1 cannot be at position 6.
Therefore, H1 is at position 1 and H5 is at position 5.
Current arrangement:
- Position 1: H1
- Position 2: H4
- Position 5: H5
- Position 6: H2
- Positions 3 and 4: H3 and H6 (in some order)
Given that H3 is towards the left of H6, H3 must be at position 3 and H6 must be at position 4.
Final arrangement:
- Position 1: H1
- Position 2: H4
- Position 3: H3
- Position 4: H6
- Position 5: H5
- Position 6: H2
Checking each option:
Option 1: H1 and H2 are at both ends → H1 at position 1, H2 at position 6 ✓ Correct
Option 2: H4 is second to the left of H6 → H4 at position 2, H6 at position 4 ✓ Correct
Option 3: H2 is to the immediate right of H5 → H5 at position 5, H2 at position 6 ✓ Correct
Option 4: H1 is towards the right of H4 → H1 at position 1, H4 at position 2 ✗ Not Correct
H1 is actually towards the left of H4, not right.
Therefore, Option 4 is NOT correct.
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