Question

В комнате собрались несколько гномов , которые всегда лгут . Все они разно- го роста и разного веса . Каждый из них сказал : « Все остальные легче меня , и кто - то из них ниже меня » . Какое из утверждений А - Г обязательно верно ? ( A Самый тяжелый гном - самый низкий . ( 5 ) Самьи легкий гном - _ самый низкий . ( B ) Самый тяжелый гном самый высокий . ( Г ) Самый легкий гном - самый высокий . ( A ) Ни одно из утверждений А - Г не обязано выполняться .

Answer 1

Для самого тяжелого фраза "Все остальные легче меня" - истина, значит, фраза "Кто-то из них ниже меня" должна быть ложью.
Значит, все выше него.
Самый тяжёлый гном - самый низкий - это истина.
Для всех остальных фраза "Все легче меня" уже ложь, поэтому о них ничего сказать нельзя.
Ответ: А)

Answer 2

Solution

To solve this problem, we can analyze the statements made by each gnome and determine which one must be true. Let's break down the statements and analyze them one by one.

1. Statement A: The heaviest gnome is the shortest. 2. Statement B: The lightest gnome is the tallest. 3. Statement C: The heaviest gnome is the tallest.

Let's analyze each statement based on the given information.

Analysis

According to the given information, each gnome makes two claims: - Claim 1: "All the others are lighter than me." - Claim 2: "At least one of them is shorter than me."

Now, let's analyze each statement:

1. Statement A: The heaviest gnome is the shortest. - If this statement is true, then the heaviest gnome must also be the shortest. This means that the heaviest gnome cannot be the tallest. - If the heaviest gnome is the shortest, then the lightest gnome must be the tallest. - This statement contradicts itself because it implies that the lightest gnome is the tallest, which is also claimed by gnome B. - Therefore, this statement cannot be true.

2. Statement B: The lightest gnome is the tallest. - If this statement is true, then the lightest gnome must also be the tallest. This means that the lightest gnome cannot be the shortest. - If the lightest gnome is the tallest, then the heaviest gnome must be the shortest. - This statement contradicts itself because it implies that the heaviest gnome is the shortest, which is also claimed by gnome A. - Therefore, this statement cannot be true.

3. Statement C: The heaviest gnome is the tallest. - If this statement is true, then the heaviest gnome must also be the tallest. This means that the heaviest gnome cannot be the shortest. - If the heaviest gnome is the tallest, then the lightest gnome must be the shortest. - This statement contradicts itself because it implies that the lightest gnome is the shortest, which is also claimed by gnome A. - Therefore, this statement cannot be true.

Conclusion

Based on the analysis, none of the statements A, B, or C can be true. All the statements lead to contradictions, and none of them can be logically true given the claims made by the gnomes.

Therefore, the correct answer is: None of the statements A, B, or C must be true.