Question

Каждый гном всегда честен или всегда лжет. В клане гномов нет двух одного возраста и нет двух с одинаковой густотой бороды. Каждый гном клана высказал два утверждения: 1) “Нет и трех гномов старше меня” 2) “Хотя бы пятеро гномов имеют более густую бороду”. Сколько гномов в клане? И могло ли это быть в принципе?​

Answer 1

Ответ:

не уверена что это правильно но попробую.

ответ:

1)всего +- 2-3 гнома.

2)в теории это бы могло бы произойти если бы

мы были в 19-20 веке. нов данный момент вера в мифологию составляет 79% от всего населения мира.

Answer 2

Problem Analysis

We are given the following information about a clan of gnomes: - Each gnome in the clan is either always honest or always lies. - No two gnomes have the same age. - No two gnomes have the same beard density.

We are also given two statements made by each gnome in the clan: 1) "There are not three gnomes older than me." 2) "At least five gnomes have a denser beard than me."

We need to determine the number of gnomes in the clan and whether it is possible for such a clan to exist.

Solution

Let's analyze the given statements and constraints to find a solution.

1) "There are not three gnomes older than me." - This statement implies that the gnome making the statement is not the oldest gnome in the clan. - If there are n gnomes in the clan, the oldest gnome's age must be n-1 or less.

2) "At least five gnomes have a denser beard than me." - This statement implies that the gnome making the statement is not one of the five gnomes with the densest beards. - If there are n gnomes in the clan, the gnome making the statement must have a beard density ranking of n-6 or lower.

Based on these constraints, let's consider the possible scenarios:

Scenario 1: There are 1 or 2 gnomes in the clan - In this scenario, there are not enough gnomes to satisfy the constraints of the statements. Therefore, this scenario is not possible.

Scenario 2: There are 3 gnomes in the clan - In this scenario, the oldest gnome can only be the gnome who made the first statement, as there are no other gnomes older than them. - The gnome who made the second statement cannot be one of the five gnomes with the densest beards, as there are only three gnomes in total. - Therefore, this scenario is not possible.

Scenario 3: There are 4 gnomes in the clan - In this scenario, the oldest gnome can only be the gnome who made the first statement, as there are no other gnomes older than them. - The gnome who made the second statement cannot be one of the five gnomes with the densest beards, as there are only four gnomes in total. - Therefore, this scenario is not possible.

Scenario 4: There are 5 or more gnomes in the clan - In this scenario, the oldest gnome cannot be the gnome who made the first statement, as there must be at least three gnomes older than them. - The gnome who made the second statement cannot be one of the five gnomes with the densest beards, as there must be at least five gnomes with denser beards. - Therefore, this scenario is not possible.

Based on the analysis, it is not possible for a clan of gnomes to exist that satisfies all the given constraints and statements.