Kvant

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A few more tasks
Vasya Smekalkina

V. M. Rosentuller

  1. 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.

  1. 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.

  2. Find the last three digits of the product of all natural numbers from 1 to 18.

  3. 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?

  4. 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

  1. 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.

  2. A multiplication action was performed on the board. Then some of the numbers were erased and replaced with asterisks. Restore erased numbers:

***
*8
***
****
****0
  1. 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?

  2. In what cases does he have 5 assistants?

  3. 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?