Kvant
Kvant for Younger Students

[Tasks]

Kvant 1971, No. 3p. 67Tag 1UNC

Rough automatic draft, low quality: expect mistakes and awkward wording. It will be replaced by a better translation. Original →

11

  1. A caterpillar is crawling along a tree. During the day it rises by 6 meters, and at night it drops by 4 meters. How many days will it take her to crawl to the top if the tree is 14 meters high?

  2. Out of 15 coins that look identical, one is counterfeit. It is unknown whether it is heavier or lighter than the others. How can you find out by doing no more than two weighings on a cup scale without mushrooms?

  3. The numbers 9 and 9 are cubes of integers. Which ones?

  4. Six matches lie on the table as shown in figure 1. You need to change their places, adhering to the following rules: a match can only be moved in the direction of its head to a free space, either by simply moving it or re-sticking it through no more than one match.

  5. Given a square sheet of paper. How can we cut it into four parts with straight lines (Fig. 2) so that they can be used to form a triangular paramid, no edges of which are equal (Fig. 3)?

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Delivered on November 24, 1970.
Signed for publication on January 28, 1971.
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