Solving the Cricket Matches Puzzle

This question requires us to deduce which person played a specific number of cricket matches based on a set of clues relating people, number of matches, and months.

Understanding the Given Information

• Five People: A, B, C, D, E
• Five Match Counts: 52, 39, 16, 75, 46
• Five Months: January (31 days), April (30 days), May (31 days), June (30 days), August (31 days)

The challenge is to match each person with a specific number of matches played and the month they played in, based on the given conditions.

Decoding the Clues Step-by-Step

Let's analyze the clues and build a sequence of people, matches, and months over the five time slots (representing the sequence in which they played):

1. "The one who played 46 matches played in the month of having 30 days." This means 46 matches were played in either April or June.
2. "The one who played 75 matches played at last." This tells us the 5th person in the sequence played 75 matches, and this happened in the last month (August, as it's the last month listed, implying an ordered sequence or the final event).
3. "E played the matches just before C." This indicates E and C are adjacent in the sequence, with E immediately preceding C (EC block).
4. "More than 2 People played between E and B." In a sequence of 5 slots, having more than 2 people between E and B means there are exactly 3 people between them. This is only possible if E is in the 1st slot and B in the 5th, OR B is in the 1st slot and E in the 5th.

Establishing the Sequence of People

Let's use the constraint "More than 2 People played between E and B" with the 5 slots:

• Possibility A: E is 1st, B is 5th (E _ _ _ B)
• Possibility B: B is 1st, E is 5th (B _ _ _ E)

Now consider the "E played just before C" clue:

• If E is 1st (Possibility A), then C must be 2nd to be immediately after E. Sequence: E, C, _, _, B.
• If E is 5th (Possibility B), then C must be 4th to be immediately before E. Sequence: B, _, _, C, E.

Next, use the clue "Only one person played between C and D".

• In the sequence E, C (2nd), _, _, B, if there is one person between C (2nd) and D, D must be in the 4th slot (2 + 2). Sequence: E, C, _, D, B.
• In the sequence B, _, _, C (4th), E, if there is one person between C (4th) and D, D must be in the 2nd slot (4 - 2). Sequence: B, D, _, C, E.

So we have two potential sequences of people:

1. E, C, ?, D, B
2. B, D, ?, C, E

The remaining person is A. Let's place A in the empty slot:

1. E, C, A, D, B
2. B, D, A, C, E

Now, check the clue "A played before B".

• Sequence 1 (E, C, A, D, B): A is 3rd, B is 5th. A played before B. This works.
• Sequence 2 (B, D, A, C, E): A is 3rd, B is 1st. A played after B. This fails the condition.

Therefore, the correct sequence of people playing is E, C, A, D, B in order of turns.

Assigning Matches and Months

Using the sequence E, C, A, D, B:

• Slot 5: B played 75 matches ("The one who played 75 matches played at last.").
• Slot 1: E
• Slot 2: C
• Slot 3: A
• Slot 4: D
• Slot 5: B (75 matches)

Clue: "16 matches played just before the one who played 46 matches." This means the person just before the one who played 46 matches played 16 matches.

Clue: "Only one person played between the one who played 46 and D." In our sequence E, C, A, D, B, D is the 4th person. There is one person (A) between the 2nd person (C) and the 4th person (D). So the person who played 46 matches must be the 2nd person, who is C. C played 46 matches.

So the assignments are:

• Slot 1: E
• Slot 2: C (46 matches)
• Slot 3: A
• Slot 4: D
• Slot 5: B (75 matches)

Now use "16 matches played just before the one who played 46 matches". The person just before C (who played 46) is E. So E played 16 matches.

Updated assignments:

• Slot 1: E (16 matches)
• Slot 2: C (46 matches)
• Slot 3: A
• Slot 4: D
• Slot 5: B (75 matches)

The matches remaining are 52 and 39. These must have been played by the remaining people, A (Slot 3) and D (Slot 4).

• A played either 52 or 39 matches.
• D played either 52 or 39 matches.

The clue "The one who played 46 matches played in the month of having 30 days" confirms that C played in April or June. The clue "The one who played 16 matches played just before the one who played 46 matches" confirms E played in the month immediately before April or June (which are January or May, respectively). The clue "The one who played 75 matches played at last" confirms B played in the last month (August). The months for A and D would be the remaining ones, but the exact match count (52 or 39) for A and D cannot be determined from the given information.

Answering the Question

The question asks who played 52 matches. Based on our deductions:

• E played 16 matches.
• C played 46 matches.
• B played 75 matches.
• A and D played the remaining matches, which are 52 and 39.

Therefore, the person who played 52 matches could be either A or D.