Question

У дядьки Черномора 30 витязей . У двадцати мз них украшены изумрудами щиты , у 15 - шлемы , у двоих нет изумрудов ни на шлемах , ни на щитах .У скольких витязей украшены одновременно изумрудами и щиты , и шлемы ?

Answer 1

30-2=28 - витязей с украшениями
(20+15)-28=7 - витязей с украшениями и щита и шлема

Answer 2

Problem Analysis

We are given that there are 30 knights, and out of them, 20 have emerald-decorated shields, 15 have helmets, and 2 have neither emeralds on their helmets nor on their shields. We need to determine how many knights have emeralds on both their shields and helmets.

Solution

Let's break down the information given: - Total number of knights: 30 - Knights with emerald-decorated shields: 20 - Knights with helmets: 15 - Knights with neither emeralds on their shields nor on their helmets: 2

To find the number of knights with emeralds on both their shields and helmets, we can use the principle of inclusion-exclusion. We'll start by adding the number of knights with emerald-decorated shields and the number of knights with helmets, and then subtract the number of knights with neither emeralds on their shields nor on their helmets.

Let's calculate it step by step:

1. Knights with emerald-decorated shields: 20 2. Knights with helmets: 15 3. Knights with neither emeralds on their shields nor on their helmets: 2

To find the number of knights with emeralds on both their shields and helmets, we'll use the formula:

Knights with emeralds on both shields and helmets = Knights with emerald-decorated shields + Knights with helmets - Knights with neither emeralds on their shields nor on their helmets

Substituting the values:

Knights with emeralds on both shields and helmets = 20 + 15 - 2 = 33

Therefore, there are 33 knights who have emeralds on both their shields and helmets.