Question

Five dogs--an Akita, a Bulldog, a Cocker Spaniel, a Doberman, and an English Settler--compete in the final round of a dog show. Each dog will be shown alone to the judges exactly once in accordance with the following conditions:

The Doberman can be shown neither immediately before nor immediately after the English Settler.
The Akita must be shown two places before the Doberman.

Which one of the following must be true?

a) If the Akita is shown third, the English Settler must be shown second.

b) If the Bulldog is shown fourth, the Akita must be shown third.

c) If the Cocker Spaniel is shown third, the English Settler must be shown first.

d) If the Doberman is shown third, the Bulldog must be shown second.

e) If the English Settler is shown second, the Cocker Spaniel must be shown fourth.

Answer 1

Upon analyzing the given conditions with respect to the options, none of the provided options must be true without additional information that was not provided. The available information is insufficient to exclusively determine a sequence that confirms one of the options as necessarily correct, as the conditions do not address some of the specific claims made in the options.

Step-by-step explanation:

The question involves the application of logical sequencing and deduction, which is a key aspect of math, particularly within the scope of logic puzzles or combinatorial games. Let's assess the given conditions and the options to determine which one must be true:

• The Doberman cannot be shown immediately before or after the English Settler.
• The Akita must be shown two places before the Doberman.

Let's analyze the options given:

• a) If the Akita is shown third, the English Settler must be shown second.
• b) If the Bulldog is shown fourth, the Akita must be shown third.
• c) If the Cocker Spaniel is shown third, the English Settler must be shown first.
• d) If the Doberman is shown third, the Bulldog must be shown second.
• e) If the English Settler is shown second, the Cocker Spaniel must be shown fourth.

Considering the condition that the Akita must be shown two places before the Doberman, let's see if option 'd' fits:

• If the Doberman is shown third, the Akita must be shown first, based on the rule that the Akita shows up two places before the Doberman.
• Giving us the sequence: Akita, X, Doberman, where X is any other dog except for the English Settler.

Since nothing in the rules specifies where the Bulldog must be shown in relation to the Doberman, option 'd' is not necessarily true. Hence, we can eliminate option d. Using a similar process for the others, we'd find that none of the given options necessarily have to be true based on the initial conditions alone, without additional information. Thus, the conditions set in the question cannot exclusively determine the correct sequence without making additional assumptions beyond the provided information.