Question

На доске записаны числа 1 2 3 4 5 6 7 8 9. Поставьте между некоторыми из них знаки «+» и «–» так, чтобы значение получившегося выражения было равно 2022, используя наименьшее количество минусов.

Answer 1

Пошаговое объяснение:

1234+5-6+789=2022

вот так вот это решается при условии, что числа менять нельзя, а можно только ставить знаки между ними

Answer 2

Problem Analysis

We are given the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 written on a board. We need to insert the symbols "+" and "-" between some of the numbers to form an expression that evaluates to 2022. The goal is to use the fewest number of "-" symbols possible.

Solution

To find a solution, we can try different combinations of inserting "+" and "-" symbols between the numbers and evaluate the resulting expression. We will start with the simplest approach and gradually increase the complexity until we find a solution.

Let's start by inserting only "+" symbols between the numbers and evaluate the expression.

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45

The sum of the numbers from 1 to 9 is 45, which is less than 2022. So, we need to introduce "-" symbols to decrease the value of the expression.

Let's try inserting a "-" symbol between the numbers 2 and 3.

1 + 2 - 3 + 4 + 5 + 6 + 7 + 8 + 9 = 39

The value of the expression is now 39. We can see that introducing a "-" symbol decreased the value of the expression. We need to continue introducing "-" symbols to further decrease the value.

Let's try inserting a "-" symbol between the numbers 4 and 5.

1 + 2 - 3 + 4 - 5 + 6 + 7 + 8 + 9 = 23

The value of the expression is now 23. We can see that introducing another "-" symbol further decreased the value of the expression.

Let's try inserting a "-" symbol between the numbers 6 and 7.

1 + 2 - 3 + 4 - 5 + 6 - 7 + 8 + 9 = 6

The value of the expression is now 6. We can see that introducing another "-" symbol further decreased the value of the expression.

Let's try inserting a "-" symbol between the numbers 8 and 9.

1 + 2 - 3 + 4 - 5 + 6 - 7 + 8 - 9 = -1

The value of the expression is now -1. We can see that introducing another "-" symbol further decreased the value of the expression.

Now, let's try inserting a "-" symbol between the numbers 1 and 2.

1 - 2 - 3 + 4 - 5 + 6 - 7 + 8 - 9 = -7

The value of the expression is now -7. We can see that introducing another "-" symbol further decreased the value of the expression.

Let's try inserting a "-" symbol between the numbers 3 and 4.

1 - 2 - 3 - 4 - 5 + 6 - 7 + 8 - 9 = -23

The value of the expression is now -23. We can see that introducing another "-" symbol further decreased the value of the expression.

Let's try inserting a "-" symbol between the numbers 5 and 6.

1 - 2 - 3 - 4 - 5 - 6 - 7 + 8 - 9 = -39

The value of the expression is now -39. We can see that introducing another "-" symbol further decreased the value of the expression.

Let's try inserting a "-" symbol between the numbers 7 and 8.

1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 = -45

The value of the expression is now -45. We can see that introducing another "-" symbol further decreased the value of the expression.

Now, let's try inserting a "-" symbol between the numbers 9 and 1.

1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 + 1 = -53

The value of the expression is now -53. We can see that introducing another "-" symbol further decreased the value of the expression.

Based on the above calculations, we can conclude that it is not possible to obtain a value of 2022 by inserting "+" and "-" symbols between the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Therefore, there is no solution to the given problem.

Conclusion

After trying different combinations of inserting "+" and "-" symbols between the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9, we found that it is not possible to obtain a value of 2022 using the given numbers and symbols.