Gymnastics for the mind: 10 fun number problems

2024 Author: Malcolm Clapton | [email protected]. Last modified: 2023-12-17 03:44

You have to arrange arithmetic signs, arrange equalities and select suitable numbers.

For convenience, we advise you to stock up on paper and a pen.

1 -

There are seven numbers: 1, 2, 3, 4, 5, 6, 7. Connect them with arithmetic signs so that the resulting expression is equal to 55. Several solutions are possible.

Here are three options for solving this problem:

1) 123 + 4 − 5 − 67 = 55;

2) 1 − 2 − 3 − 4 + 56 + 7 = 55;

3) 12 − 3 + 45 − 6 + 7 = 55.

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2-

In the expression 5 × 8 + 12 ÷ 4 - 3, place the parentheses so that its value is 10.

(5 × 8 + 12) ÷ 4 - 3. Check if the value of the expression is actually 10. Perform the actions in parentheses, then division and subtraction: (40 + 12) ÷ 4 - 3 = 52 ÷ 4 - 3 = 13 - 3 = 10.

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3 -

Compose an expression of seven fours, arithmetic signs and a comma so that its value is 10.

44, 4 ÷ 4 - 4, 4 ÷ 4. Check the obtained expression by first performing division and then subtracting: 11, 1 - 1, 1 = 10.

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4 -

If we multiply these three integers, then the result will be the same as if we were adding them. What are these numbers?

The numbers 1, 2, 3, when multiplied and added, give the same result: 1 + 2 + 3 = 6; 1 × 2 × 3 = 6.

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5 -

The number 9, with which the three-digit number began, was moved to the end of the number. The result is a number that is 216 less. Find the original number.

Let 9AB be the original number, then AB9 is the new number. Following the conditions of the problem, we compose the following equality: 216 + AB9 = 9AB.

Let's find the number of ones: 6 + 9 = 15, therefore B = 5. Substitute the obtained value into the expression: 216 + A59 = 9A5. Let's find the number of hundreds: 9 - 2 = 7, which means A = 7. Let's check: 216 + 759 = 975. This is the original number.

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6 -

If you subtract 7 from the planned three-digit number, then it will be divided by 7; if you subtract 8, it is divided by 8; if you subtract 9, it will be divided by 9. Find this number.

To determine the intended number, you need to calculate the least common multiple of 7, 8 and 9. To do this, multiply these numbers together: 7 × 8 × 9 = 504. Let's check if this number is right for us:

504 − 7 = 497; 497 ÷ 7 = 71;

504 − 8 = 496; 496 ÷ 8 = 62;

504 − 9 = 495; 495 ÷ 9 = 55.

This means that the number 504 satisfies the condition of the problem.

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7 -

Look at the equality 101 - 102 = 1 and rearrange one digit so that it is correct.

101 − 10² = 1. Let's check: 101 - 100 = 1.

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8 -

99 numbers are written down: 1, 2, 3, … 98, 99. Count how many times the number 5 appears in this string.

20 times. Here are the numbers that satisfy the condition: 5, 15, 25, 35, 45, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 65, 75, 85, 95.

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9 -

Answer how many two-digit numbers there are with the tens digit less than the ones digit.

To find a solution, we will reason as follows: if there is a number 1 in the place of tens, then in the place of ones there is any of the numbers from 2 to 9, and these are eight options. If the tens place contains the number 2, then the ones place contains any of the numbers from 3 to 9, and these are seven options. If in the tens place is the number 3, then in the ones place there is any of the numbers from 4 to 9, and these are six options. Etc.

Let's calculate the total number of combinations: 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 36.

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10 -

In the number 3 728 954 106, remove the three digits so that the remaining digits in the same order represent the smallest seven-digit number.

For the desired number to be the smallest, it is necessary that it begins with the smallest possible digit, so we remove the numbers 3 and 7. Now we need the smallest digit after the two. If you cross out the eight, a nine will appear in its place and the number will increase. Therefore, we remove 9. This is the number we get: 2 854 106.

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