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Gymnastics for the mind: 10 fun number problems
Recreation / / December 31, 2020
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 55. Several solutions are possible.
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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.
— 2—
In the expression 5 × 8 + 12 ÷ 4 - 3, place the brackets so that its value is 10.
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(5 × 8 + 12) ÷ 4 − 3. Let's check if the value of the expression is really 10. Let's perform the actions in brackets, then division and subtraction: (40 + 12) ÷ 4 - 3 = 52 ÷ 4 - 3 = 13 - 3 = 10.
— 3 —
Make up an expression of seven fours, arithmetic signs and a comma so that its value is 10.
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44,4 ÷ 4 − 4,4 ÷ 4. Let's check the resulting expression by first performing division and then subtracting: 11.1 - 1.1 = 10.
— 4 —
If we multiply these three integers, then the result will be the same as if we were adding them. What are these numbers?
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The numbers 1, 2, 3, when multiplied and added, give the same result: 1 + 2 + 3 = 6; 1 × 2 × 3 = 6.
— 5 —
The number 9, with which the three-digit number began, was moved to the end of the number. The result is 216 less. Find the original number.
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Let 9AB be the original number, then AB9 is the new number. Following the conditions of the problem, we make the following equality: 216 + AB9 = 9AB.
Let's find the number of ones: 6 + 9 = 15, so B = 5. Let's substitute the obtained value into the expression: 216 + A59 = 9A5. Let's find the number of hundreds: 9 - 2 = 7, so A = 7. Let's check: 216 + 759 = 975. This is the original number.
— 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 take away 9 - will be divided by 9. Find this number.
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To determine the intended number, you need to calculate the least common multiple of 7, 8, and 9. To do this, we multiply these numbers with each other: 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.
Hence, the number 504 satisfies the condition of the problem.
— 7 —
Look at the equality 101 - 102 = 1 and rearrange one digit so that it is correct.
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101 − 102 = 1. Let's check: 101 - 100 = 1.
— 8 —
99 numbers are written down: 1, 2, 3,... 98, 99. Count how many times the number 5 appears in this string.
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19 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.
— 9 —
Answer how many two-digit numbers, in which the tens digit is less than the ones digit.
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To find a solution, we will reason as follows: if there is a number 1 in the tens place, then in the ones place 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.
— 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.
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For the desired number to be the smallest, you need it to start with the smallest possible digit, so we remove the numbers 3 and 7. Now we need the smallest number 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. Here's the number you get: 2 854 106.
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