Question

Скольким способами из цифр от 0 до 9 можно поставить два четырёхзначных числа и одно двузначное число таким образом чтобы их сумма была наименьшей из возможных? Чему равна эта сумма?

Answer 1

Ответ:

20112202102

Пошаговое объяснение:

20112202102

Answer 2

Problem Analysis

To find the two four-digit numbers and one two-digit number such that their sum is the smallest possible, we need to consider the following: - The four-digit numbers can be formed using the digits from 0 to 9. - The two-digit number can also be formed using the digits from 0 to 9. - We want to minimize the sum of these three numbers.

Solution

To minimize the sum, we can start by assigning the smallest possible digits to the most significant places in the four-digit numbers. This will ensure that the sum remains as small as possible.

Let's go step by step:

1. For the first four-digit number, we can assign the digit 0 to the thousands place. This will make it the smallest possible four-digit number. 2. For the second four-digit number, we can assign the digit 1 to the thousands place. This will make it the second smallest four-digit number. 3. For the two-digit number, we can assign the digit 2 to the tens place. This will make it the smallest possible two-digit number.

So, the three numbers are: - First four-digit number: 0XYZ - Second four-digit number: 1UVW - Two-digit number: 2AB

Now, let's assign the remaining digits to the respective places in these numbers.

For the first four-digit number: - The digit X can be any digit from 0 to 9, excluding 0. - The digit Y can be any digit from 0 to 9, excluding 0 and X. - The digit Z can be any digit from 0 to 9, excluding 0, X, and Y.

For the second four-digit number: - The digit U can be any digit from 0 to 9, excluding 1. - The digit V can be any digit from 0 to 9, excluding 1 and U. - The digit W can be any digit from 0 to 9, excluding 1, U, and V.

For the two-digit number: - The digit A can be any digit from 0 to 9, excluding 2. - The digit B can be any digit from 0 to 9, excluding 2 and A.

Now, let's calculate the sum of these three numbers.

Calculation

The sum of the three numbers can be calculated as follows:

Sum = 0XYZ + 1UVW + 2AB

Since we want to minimize the sum, we need to assign the smallest possible values to X, Y, Z, U, V, W, A, and B.

The smallest possible values for these digits are: - X = 1 - Y = 2 - Z = 3 - U = 0 - V = 4 - W = 5 - A = 6 - B = 7

Substituting these values into the sum equation, we get:

Sum = 0123 + 1045 + 267

Calculating the sum, we find:

Sum = 2188 + 1045 + 267 = 3500

Therefore, the sum of the two four-digit numbers and one two-digit number, such that their sum is the smallest possible, is 3500.

Conclusion

To minimize the sum of the two four-digit numbers and one two-digit number, we assign the smallest possible digits to the most significant places in the four-digit numbers. The sum of these three numbers is 3500.