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A few more tasks
Vasya Smekalkina
V. M. Rosentuller
- Given a series of integers, which is composed according to a certain mathematical law:
4, 7, 12, 21, 38, …
Continue the series until you reach the eighth number.
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The sum of the minuend, subtrahend and difference is 624. Find the minuend, subtrahend and difference if the difference is 56 less than the subtrahend.
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Find the last three digits of the product of all natural numbers from 1 to 18.
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There are two vessels with a capacity of 3 liters and 5 liters. How can you use these vessels to find 4 liters of water from a tap?
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In the table of calculations according to some rule. Find this rule and subtract the missing numbers.
a) 2 3 5 9 33
b) 1 5 6 11 28
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The store has mastic in boxes of 16 k, 17 k and 21 k. How can one organization get 185 ke of mastic without opening the boxes? Find all solutions.
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A multiplication action was performed on the board. Then some of the numbers were erased and replaced with asterisks. Restore erased numbers:
***
*8
***
****
****0
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The student bought 4 books. All books without the first cost 42 kopecks, without the second - 40 kopecks, without the third - 38 kopecks, without the fourth - 36 kopecks. How much does each book cost?
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In what cases does he have 5 assistants?
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There are 15 pencils on the table. Two people take turns taking one, two or three pencils. The one who has one last pencil left to take loses. How should a beginner play the game so that he forces his opponent to take the last pencil?