Read the given information carefully and answer the questions based on it:
Six persons visit a place on two dates 11 and 22 in three different months i.e., September, October and November. They all like different colors viz. white, blue, pink, green, red and yellow but not necessarily in the same order as given.
The one who likes yellow visits three persons after L. L and S visit on same date and in the month of even numbered days. Two persons visit between S and R who likes green. Number of persons visit before R is same as the number of persons visit after V. The one who likes white visit just before H. No one visit between K and the one who likes blue. The one who likes red visits before the one who likes pink.
How many persons visit between K and H?
Correct Answer :
Three
Solution :
To find the number of persons who visit between K and H, let us systematically analyze the given information and reconstruct the visiting schedule of the six persons.
1. Identify the Schedule Structure:
There are three months: September (30 days), October (31 days), and November (30 days).
The visits occur on two dates: 11th and 22nd.
This gives us a total of 6 slots in chronological order:
1) September 11
2) September 22
3) October 11
4) October 22
5) November 11
6) November 22
2. Analyze the Clues to Place the Persons and Colors:
• "L and S visit on same date and in the month of even numbered days."
The months with even numbered days (30 days) are September and November. Therefore, L and S must visit on the same date (either both on the 11th or both on the 22nd) in September and November.
This means one of them visits in September and the other in November, on the same date (11th or 22nd).
• "The one who likes yellow visits three persons after L."
"Three persons after L" means if L is at position X, the person who likes yellow is at position X + 3.
Since the yellow-liking person is at X + 3, L's position can only be 1 (Sept 11), 2 (Sept 22), or 3 (Oct 11).
However, we already know L must visit in a 30-day month (September or November). Thus, L must be in September (positions 1 or 2).
Let's consider the two possibilities for L's date:
- Case A: L visits on September 11 (Position 1). Then S visits on November 11 (Position 5) because they visit on the same date in the even-day months. The person who likes yellow visits 3 positions after L, which is Position 4 (October 22).
- Case B: L visits on September 22 (Position 2). Then S visits on November 22 (Position 6). The person who likes yellow visits 3 positions after L, which is Position 5 (November 11).
• "Two persons visit between S and R who likes green."
- In Case A: S is at Position 5. Two persons between S and R means R must be at Position 2 (September 22). R likes green.
- In Case B: S is at Position 6. Two persons between S and R means R must be at Position 3 (October 11). R likes green.
• "Number of persons visit before R is same as the number of persons visit after V."
- In Case A: R is at Position 2 (1 person before R). So, 1 person must visit after V, which means V is at Position 5. But S is already at Position 5. This creates a conflict. So, Case A is invalid.
- In Case B: R is at Position 3 (2 persons before R). So, 2 persons must visit after V, which means V is at Position 4 (October 22). This is valid.
Let's continue with Case B:
L is at Position 2 (September 22).
S is at Position 6 (November 22).
R is at Position 3 (October 11) and likes green.
V is at Position 4 (October 22).
The person who likes yellow is at Position 5 (November 11).
Currently, the remaining positions to be filled by persons are Position 1 (September 11) and Position 5 (November 11). The remaining persons are K and H.
• "The one who likes white visit just before H."
Since the white-liker visits just before H, H cannot be at Position 1. Therefore, H must be at Position 5 (November 11). This leaves K to be at Position 1 (September 11).
Since H is at Position 5, the person who visits just before H is at Position 4 (V). Thus, V must like white.
Since H is at Position 5, and we determined earlier that the person at Position 5 likes yellow, H likes yellow.
Now we have the positions of all six persons:
1) K (September 11)
2) L (September 22)
3) R (October 11) - Green
4) V (October 22) - White
5) H (November 11) - Yellow
6) S (November 22)
• Let's verify the remaining color clues to make sure the arrangement is fully consistent:
- "No one visit between K and the one who likes blue."
This means the one who likes blue is next to K. Since K is at Position 1, the person at Position 2 (L) must like blue.
- "The one who likes red visits before the one who likes pink."
The remaining colors are red and pink. The remaining positions for these colors are Position 1 (K) and Position 6 (S). Since red visits before pink, K (Position 1) likes red, and S (Position 6) likes pink.
This completely and consistently satisfies all clues.
3. Answer the Question:
We need to find the number of persons who visit between K and H.
K visits at Position 1 (September 11).
H visits at Position 5 (November 11).
The persons visiting between them are at Positions 2, 3, and 4 (L, R, and V).
Therefore, there are exactly three persons (L, R, and V) visiting between K and H.
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