Question

What is Amda's score in F?

• A. 14
• B. 15
• C. 16
• D. 17
• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Correct Answer: 1

The provided information can be depicted in the following table.
Amda's Score Determination 

Step 1: Recap of A and C's total

We know:

• A and C jointly obtained a total score of 7.
• They had equal scores in all parameters.

Possible equal-score distributions are: \[ (1, 2, 4) \quad \text{or} \quad (3, 3, 1) \]

 

Step 2: Zooma’s fixed distribution

Zooma’s total score is 17. Since each country in the happy category secured the highest score in exactly one parameter, Zooma can have: \[ F = 7, \quad S = 6, \quad C = 4 \] Why this works:

• 7 in S and 6 in C would belong to other countries’ top scores, so they are not assigned to Zooma.
• Distribution \( (7, 7, 5) \) is invalid because no country scored 5 in C.

Step 3: Possible distributions for Amda

Given the remaining scoring rules, Amda can only have: \[ (3, 3, 1) \quad \text{or} \quad (4, 2, 1) \]

Step 4: Restriction on the score of 1

Observation: No other parameter (S or C) has a score of 1 for two different countries. Thus, the score of 1 for Amda must occur in **F**.

Final Conclusion:

Amda’s possible score distributions are: \[ (F, S, C) = (1, 3, 3) \quad \text{or} \quad (1, 4, 2) \] with \(F = 1\) being the fixed point across both cases.

Answer 2

The provided information can be depicted in the following table.

 

Determining Zooma’s Scores

Step 1: Joint score of A and C

We know:

• A and C jointly obtained a total score of 7 in all parameters.
• Their scores in each parameter were equal.

Thus, the possible equal-score combinations are: \[ (1, 2, 4) \quad \text{or} \quad (3, 3, 1) \]

Step 2: Zooma’s total score constraint

Zooma’s total score is: \[ F + S + C = 17 \] Zooma is in the "happy" category, and each happy country scored the highest in exactly one parameter.

Step 3: Excluding impossible score distributions

• If Zooma had 7 in S and 6 in C, these would be the top scores for other countries, which is not allowed for Zooma.
• The combination \( (7, 7, 5) \) is impossible because no country scored a 5 in C.

Step 4: Corrected assignment

From earlier deductions and category rules, Zooma’s score in C is fixed at: \[ \boxed{C = 6} \] Given the total of 17, the remaining F and S scores must sum to: \[ F + S = 11 \] and must follow the "highest score in exactly one parameter" rule for Zooma.

Final Conclusion:

Zooma’s scores are consistent with: \[ F = 7, \quad S = 4, \quad C = 6 \] or another valid split of \(F + S = 11\) satisfying the category constraints.

Answer 3

The provided information can be depicted in the following table.

A and C jointly obtained a total score of 7, with equal scores in all these parameters. Therefore, the possible combinations are either 1, 2, and 4 or 3, 3, and 1. Since Zooma has a score of 17, and all three countries in the happy category secured the highest score in exactly one parameter, Zooma can have a score of 7 in F, 6 in S, and 4 in C. This is because a score of 7 in S and 6 in C would be the scores of the other two countries, and Zooma cannot have a distribution of 7, 7, and 5, as there is no country that scored a 5 in C.
In the provided table, Zoom achieved the highest scores with 7 in F, 6 in S, and 4 in C. The optimal remaining scores for Benga and Dalma could be:

As it is given that both had the same total score, it can only be 15 for both, i.e., Benga’s score in S or F was one less than the maximum possible.

Answer 4

The provided information can be depicted in the following table.

Step 1: Scores of A and C

We are told that:

• A and C jointly obtained a total score of 7.
• They had equal scores in all parameters.

Possible equal-score combinations across the parameters are: \[ (1, 2, 4) \quad \text{or} \quad (3, 3, 1) \]

 

Step 2: Constraints from the "happy" category

- Zooma’s total score = 17. - All three countries in the happy category achieved the highest score in exactly one parameter.

Step 3: Assigning Zooma's scores

If Zooma is in the happy category, then:

• Zooma can have 7 in F, 6 in S, and 4 in C.
• A 7 in S and 6 in C would correspond to other countries' maximum scores, so Zooma can't have both of them.
• A distribution of \( (7, 7, 5) \) is not possible because there is no country that scored a 5 in C.

Step 4: Considering total scores

Given: \[ \text{Zoom} = 17, \quad \text{Benga} = 16, \quad \text{Delma} = 15 \] This distribution fits the conditions derived above and satisfies the total score requirements.

Final Deduction:

\[ \boxed{\text{Zooma: } (F=7, \ S=6, \ C=4), \quad \text{Benga: } 16, \quad \text{Delma: } 15} \]

If Benga scores 16 and Dalma scores 15 (as illustrated in the previous solution), the highest possible values that remain are: