A child's task that only former excellent students can easily understand

One who believes that mathematics is interesting and useful only for schoolchildren or students is mistaken. Adults also like to solve problems. So today's editorial office. "Site" Readers will learn a couple of interesting things. Test your strength and find it. shortcut. Good guys do it fast. Can you do it?



Brief solution of the problem

1. Uncle Grisha's nephews came to the village. Seeing various animals in his yard, they asked how many geese he had. The owner of the site said that if you take into account only his cats and geese, you can count 7 heads and 24 legs. Can you tell me how many geese Uncle Grisha has?
   
   
   
   
2. In the conditions of the second problem, it is indicated that there were a number of sparrows that sat on poles. A passer-by noticed that if two sparrows sat on each pillar, one pillar would remain empty. And if the sparrows were seated on poles one by one, then one sparrow would be superfluous. How many pillars were there, and how many sparrows?
   
   
   
   
3. To climb from the first floor to the third floor, you need to overcome 30 steps. How many steps do you have to climb to the 9th floor of the same house? Try counting all the steps quickly. Check out our answers in the second part of the article.
   
   
   
   

Tips and answers to problems

1. A cat has one head and four legs, and a goose has one head and two legs. We hope all our readers know what these animals look like. Cats are not 7 (otherwise there would be 28 legs) or 6 (otherwise one head would be superfluous). Here are 5 cats and 2 geese. Then the number of legs (24) and the number of heads (7) will coincide.
   
   
   
   
2. Obviously there are more than two sparrows. And if they can sit on pillars of two, then there are 4 or more. If we assume that there are 4 sparrows, then there should be 3 pillars (so that during a single seating one sparrow would be without a pole). And if the sparrows sit in pairs, they will actually occupy only two pillars, and one will be empty. There are 3 pillars and 4 sparrows.
3. Someone hastens to multiply 30 steps by 3 and makes a mistake. After all, from the first floor to the third there are only two spans, and from the first to the ninth - 8 spans. Therefore, you need (8 ÷ 2) × 30 = 4 × 30 = 120 steps. That is how many steps you need to overcome to walk from the first floor to the ninth. It is better to use the elevator.
   
   
   
   

Did you manage to solve the problems? Well, congratulations, then. However, do not rush to pick your nose up, because we have puzzles and more complicated ones. Try to deal with them, too. And also solve fascinating school examples that can only be solved by round excellent students.