Question

Капитан Кук попал в плен к пиратам. Их главарь требует у него выкуп, причем, хочет получить требуемую сумму ровно 13 монетами. Сможет ли Кук откупиться, если сумма выкупа - 100 дублонов, а у него есть монеты в 1,3,5 и 25 дублонов

Answer 1

В 1-м уравнении в правой части стоит нечетное число. Значит, в левой части одно или три нечетных числа.
Тогда во 2-м уравнении в левой части тоже будут одно или три нечетных числа (так как все коэффициенты нечетные) . В сумме они дадут нечетное число. Так как число 100 - четное
А значит Куку Кердык!))

Answer 2

Can Captain Cook ransom himself from the pirates?

Captain Cook is being held captive by pirates who are demanding a ransom of exactly 13 coins. The total ransom amount is 100 doubloons, and Captain Cook has coins in denominations of 1, 3, 5, and 25 doubloons. Let's determine if Captain Cook can ransom himself using the available coins.

To find out if Captain Cook can pay the ransom, we need to check if there is a combination of coins that adds up to 100 doubloons and includes exactly 13 coins.

Let's consider the possible combinations of coins that Captain Cook can use to pay the ransom:

1. Using only 1 doubloon coins: - The maximum number of 1 doubloon coins Captain Cook can use is 100, which would give a total of 100 doubloons. However, this would exceed the required ransom amount of 100 doubloons. - Therefore, using only 1 doubloon coins is not a valid combination.

2. Using only 3 doubloon coins: - The maximum number of 3 doubloon coins Captain Cook can use is 33, which would give a total of 99 doubloons. However, this would not reach the required ransom amount of 100 doubloons. - Therefore, using only 3 doubloon coins is not a valid combination.

3. Using only 5 doubloon coins: - The maximum number of 5 doubloon coins Captain Cook can use is 20, which would give a total of 100 doubloons. However, this would require 20 coins, which exceeds the required number of 13 coins. - Therefore, using only 5 doubloon coins is not a valid combination.

4. Using only 25 doubloon coins: - The maximum number of 25 doubloon coins Captain Cook can use is 4, which would give a total of 100 doubloons. However, this would require 4 coins, which is less than the required number of 13 coins. - Therefore, using only 25 doubloon coins is not a valid combination.

5. Using a combination of different coin denominations: - Captain Cook can use a combination of 3 doubloon coins and 25 doubloon coins to make up the required ransom amount of 100 doubloons. However, this combination would require a total of 7 coins (4 coins of 25 doubloons and 3 coins of 3 doubloons), which is less than the required number of 13 coins. - Therefore, using a combination of different coin denominations is not a valid combination.

Based on the available coins and their denominations, Captain Cook does not have a valid combination of coins that can be used to pay the ransom of exactly 13 coins and a total of 100 doubloons. Therefore, Captain Cook cannot ransom himself from the pirates with the given coins.