Question

Никита написал два нечетных числа а потом заменил У них разные цифры разными буквами а одинаковые - одинаковыми У Никиты получилось два слова : Учителя и мечтатели Известно что произведение цифр числа Учителя не равно нулю а произведение цифр числа мечтатели мечтатели равно нулю. Чётной или нечётной будет сумма Я+И+Мечта?ответ нужно обосновать

Answer 1

Учителя: 1234567 - произведение цифр не равно 0

Мечтатели: 852404563 - произведение цифр равно 0

Я + И + Мечта = 7 + 3 + 85240 = 85250 - чётная сумма

Answer 2

Problem Analysis

- Nikita wrote two odd numbers and replaced the digits with different letters, except for the same digits which were replaced with the same letter. - The two words formed by the replaced digits are "Учителя" (Teachers) and "мечтатели" (Dreamers). - The product of the digits of "Учителя" is not zero, while the product of the digits of "мечтатели" is zero. - The question is whether the sum of the digits of "Я" (I) + "И" (And) + "Мечта" (Dream) is even or odd.

Solution

To determine whether the sum of the digits of "Я" + "И" + "Мечта" is even or odd, we need to analyze the digits in each word.

1. Учителя (Teachers): - The product of the digits is not zero. - We don't have the actual digits or letters, so we cannot determine the sum of the digits.

2. мечтатели (Dreamers): - The product of the digits is zero. - Since the product is zero, at least one of the digits must be zero. - Therefore, the sum of the digits in "мечтатели" is even.

Based on the above analysis, the sum of the digits of "Я" + "И" + "Мечта" is even.

Please note that without the actual digits or letters used by Nikita, we cannot determine the exact sum of the digits. However, based on the given information, we can conclude that the sum is even.