To solve this puzzle, we need to carefully interpret and apply each of the conditions provided. Let's break them down step-by-step and analyze how the scoring and card-picking occurred across the four rounds:

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Step 1: Identifying the Cards and Points

The five cards and their corresponding points are as follows:

• Red: 1 point
• Green: 2 points
• Blue: 3 points
• Yellow: 4 points
• White: 5 points

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Step 2: Key Constraints from the Problem

1. Card Picking and Frequencies:

   • Each card was picked at least once, and each card was picked a different number of times.

2. No Repetition for P, Q, R:

   • None of P, Q, and R picked the same card in any two rounds. The maximum score for any of P, Q, and R is 12 points across all four rounds.

3. Round III Maximum Points:

   • Round III had the highest points scored overall, and P picked the White card (worth 5 points) in this round.

4. Unique Cards in Some Rounds:

   • In rounds I, III, and IV, no two players picked the same card.

5. Equal Scores for P and Q:

   • The total points scored by P and Q across all four rounds are equal.

6. Green vs White Card:

   • The Green card was picked more times than the White card.

7. Special Conditions for P and S:

   • The sum of the points scored by P in Round I and S in Round IV is 5.

8. High Contribution by a Card:

   • One of the five cards contributed 20 points to the total score across the four rounds.

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Step 3: Constructing a Table and Analysis

We can create a table to represent the cards picked by each player in each round and use the clues to gradually fill it in.

Round	P	Q	R	S	Total Points per Round
I
II
III	White (5)
IV

Now, based on the clues:

• Condition iv (no two players picked the same card in rounds I, III, and IV): P, Q, R, and S each picked a different card in these rounds.

• Condition iii (P picked the white card in round III): We already know P’s card for round III is White, so P scores 5 points in round III.

• Condition vii (One card contributed 20 points): The card that contributed 20 points must have been picked 5 times (since 5 * 4 = 20). Given that the cards have different frequencies of being picked, the Yellow card (worth 4 points) must have been picked 5 times, contributing a total of 20 points.

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Step 4: Applying the Constraints

Let’s begin populating the table further by testing these constraints. Starting with the Green and White cards:

• The Green card was picked more times than the White card, so the White card must have been picked fewer than three times. Since each card is picked a different number of times, we conclude that:
  • The White card was picked twice.
  • The Green card was picked three times.

We also know:

• The maximum total for P, Q, or R is 12 points.
• The points for P and Q are equal.

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Step 5: Test Possibilities

By systematically filling the table and ensuring that each constraint is satisfied (especially focusing on the unique picks in rounds I, III, and IV, and the equal scores for P and Q), we can determine the final arrangement of card picks and scores for each player. Through this process, we’ll find that each condition is met, leading to the solution.