Question

Маша сказала Саше, что задумала два различных натуральных числа, больших 17. Потом она сообщила Саше их сумму. − Я не знаю задуманные числа, − сказал на это Саша. − Как минимум одно из них — четное, − ответила Маша. − Теперь я точно знаю задуманные числа, − обрадовался Саша. Какие числа задумала Маша? Введите их в любом порядке

Answer 1

Ответ:

Пошаговое объяснение:

натуральные числа разные и больше 17 значит сумма не меньше 18+19=37

если искать различные варианты суммы двух различных натуральных чисел то мы видим что

37=18+19 - единственный вариант (не удовлетворяет условию)

38 = 18+20 - единственный вариант (не удовлетворяет условию)

39 = 18+21=19+20 - в обоих присутствуют четные слагаемые

40 = 18+22=19+21 - бинго ! два варианта и лишь один содержит хоть одно четное слагаемое

ответ 18 + 22

Answer 2

Problem Analysis

Masha has chosen two different natural numbers greater than 17. She then tells Sasha the sum of these numbers. Sasha initially doesn't know the chosen numbers, but Masha gives him a clue that at least one of the numbers is even. After receiving this clue, Sasha is able to determine the chosen numbers. We need to find out what numbers Masha chose.

Solution

Let's consider the possible scenarios and analyze them step by step:

1. If the sum of the two numbers is odd, then both numbers must be odd. This is because the sum of an odd number and an even number is always odd. However, Masha stated that at least one of the numbers is even, so this scenario is not possible.

2. If the sum of the two numbers is even, then at least one of the numbers must be even. This is because the sum of two odd numbers is always even. Since Masha stated that at least one of the numbers is even, this scenario is possible.

Based on the above analysis, we can conclude that the sum of the two numbers is even and at least one of the numbers is even.

Now, let's find the possible values for the chosen numbers:

- Since the sum of the two numbers is even, one number must be even and the other number must be odd.

- The smallest even number greater than 17 is 18.

- To find the odd number, we subtract 18 from the sum that Masha told Sasha.

Let's calculate the possible values for the chosen numbers:

- Masha told Sasha the sum of the two numbers.

- Sasha subtracted 18 from the sum to find the odd number.

- The remaining number is the even number.

Let's calculate the possible values for the chosen numbers:

1. Suppose Masha told Sasha that the sum is 40.

- Sasha subtracts 18 from 40 and gets 22.

- The possible numbers are 18 and 22.

2. Suppose Masha told Sasha that the sum is 50.

- Sasha subtracts 18 from 50 and gets 32.

- The possible numbers are 18 and 32.

Therefore, the possible numbers that Masha chose are 18 and 22 or 18 and 32.