Question

В обороте участвуют монеты достоинством 1 рубль, 2 рубля, 5 рублей и 10 рублей. Сколькими способами можно набрать сумму 66 рублей?

Answer 1

1) 66*1 - 1 набор.
2) 64*1 + 2, 62*1 + 2*2, 60*1 + 3*2, ..., 33*2 - 33 набора
3) 61*1 + 5, 56*1 + 2*5, 51*1 + 3*5, ..., 1 + 13*5 - 13 наборов
4) 59*1 + 1*2 + 1*5, 57*1 + 2*2 + 1*5, ..., 1 + 30*2 + 1*5 - 30 наборов
И так далее, все наборы посчитать очень сложно.

Answer 2

Calculating the Number of Ways to Make 66 Rubles

To calculate the number of ways to make a sum of 66 rubles using coins of 1 ruble, 2 rubles, 5 rubles, and 10 rubles, we can use a combination of mathematical principles.

Let's break down the problem step by step:

1. Start by considering the number of 10-ruble coins. Since the sum is 66 rubles, the maximum number of 10-ruble coins that can be used is 6 (6 x 10 = 60). We can use 0, 1, 2, 3, 4, 5, or 6 10-ruble coins.

2. After determining the number of 10-ruble coins, we need to calculate the remaining sum. In this case, the remaining sum is 66 - (10 x number of 10-ruble coins).

3. Now, let's consider the number of 5-ruble coins. Since the remaining sum is less than or equal to 50 (5 x 10), the maximum number of 5-ruble coins that can be used is 10 (10 x 5 = 50). We can use 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10 5-ruble coins.

4. After determining the number of 5-ruble coins, we need to calculate the remaining sum. In this case, the remaining sum is (66 - (10 x number of 10-ruble coins)) - (5 x number of 5-ruble coins).

5. Finally, let's consider the number of 2-ruble coins. Since the remaining sum is less than or equal to 20 (2 x 10), the maximum number of 2-ruble coins that can be used is 33 (33 x 2 = 66). We can use 0, 1, 2, 3, ..., 33 2-ruble coins.

6. After determining the number of 2-ruble coins, we need to calculate the remaining sum. In this case, the remaining sum is ((66 - (10 x number of 10-ruble coins)) - (5 x number of 5-ruble coins)) - (2 x number of 2-ruble coins).

7. Finally, the remaining sum can be represented by the number of 1-ruble coins. Since the remaining sum is less than or equal to 66 (1 x 66), the maximum number of 1-ruble coins that can be used is 66