Seven persons A, B, C, D, E, F and G sit in a row facing north. They have different elements named copper, nickel, gold, mercury, aluminum, silver and iron. The information is not used in the same order as given. The one who have gold sits third to the left of D, none of them sits at any of the extreme ends. E sits immediate right of the one who have gold. B and E sit adjacent to each other. The one who have iron sits second to the left of B. Two persons sit between G and F. The one who has mercury sits fourth to the right of G. The one who have copper sits immediate right of the one who has silver. The one who have nickel sits to the left of F and to the right of A.
How many persons sit to the left of the one who have copper?
Correct Answer :
Four
Solution :
The correct answer is Four.
Let us analyze and solve the puzzle step-by-step by placing the seven persons (A, B, C, D, E, F, G) and their respective elements (copper, nickel, gold, mercury, aluminum, silver, iron) in seven positions from left to right, numbered 1 to 7.
Step 1: Determine the positions of Gold and D
According to the clues:
- The one who has gold sits third to the left of D.
- Neither of them sits at any of the extreme ends (positions 1 and 7).
This gives us two possible scenarios:
- Case 1: Gold is at position 2, and D is at position 5.
- Case 2: Gold is at position 3, and D is at position 6.
Step 2: Place E, B, and Iron
- E sits immediate right of the one who has gold. So, E is at (Gold's position + 1).
- B and E sit adjacent to each other.
- The one who has iron sits second to the left of B. This means B's position must be at least 3, and the person at (B's position - 2) has iron.
Let's test Case 1:
- Gold is at 2, E is at 3, and D is at 5.
- Since B is adjacent to E (at 3), B can be at 2 or 4. But if B is at 4, the person at position 2 (who has Gold) must have Iron. This is a contradiction since each person has a unique element. If B is at 2, it is also invalid as there is no position 0 for Iron. Thus, Case 1 is eliminated.
Let's test Case 2:
- Gold is at 3, E is at 4, and D is at 6.
- Since B is adjacent to E (at 4), B can be at 3 or 5.
- If B is at 5, then the person at position 3 (who has Gold) must have Iron, which is a contradiction. Thus, B must be at position 3 (which corresponds to Gold).
- The person at position 1 (3 - 2 = 1) has Iron.
So, the arrangement so far is:
- Position 1: Iron
- Position 2: [Empty]
- Position 3: B (Gold)
- Position 4: E
- Position 5: [Empty]
- Position 6: D
- Position 7: [Empty]
Step 3: Place G, F, and Mercury
- The one who has mercury sits fourth to the right of G (Mercury is at G + 4).
- Two persons sit between G and F (F is at G + 3 or G - 3).
- Since Mercury must be at G + 4, G can only be at position 2 (so Mercury is at 6, which is D). If G were at 1, F would need to be at 4, which is already occupied by E.
- Thus, G is at position 2, D (at 6) has Mercury, and F is at position 5 (2 + 3 = 5).
The arrangement now is:
- Position 1: [Person A/C], Iron
- Position 2: G, [Element]
- Position 3: B, Gold
- Position 4: E, [Element]
- Position 5: F, [Element]
- Position 6: D, Mercury
- Position 7: [Person A/C], [Element]
Step 4: Place Silver, Copper, Nickel, and A
- The one who has copper sits immediate right of the one who has silver. The only two adjacent vacant element spots are at positions 4 and 5. Therefore, E (at 4) has Silver, and F (at 5) has Copper.
- The one who has nickel sits to the left of F (at 5) and to the right of A. The only vacant element spot to the left of F is position 2. So, G (at 2) has Nickel.
- Since Nickel (at 2) is to the right of A, A must be at position 1. By elimination, C is at position 7 (with the remaining element, Aluminum).
Final Arrangement:
- Position 1: A (Iron)
- Position 2: G (Nickel)
- Position 3: B (Gold)
- Position 4: E (Silver)
- Position 5: F (Copper)
- Position 6: D (Mercury)
- Position 7: C (Aluminum)
Conclusion:
The one who has copper is F, who sits at position 5. The persons sitting to the left of F are A, G, B, and E (4 persons in total).
Therefore, four persons sit to the left of the one who has copper.
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