# Problem 5.

B-1

Chicks hatch on the night from Sunday to Monday. For two weeks, the chick sits with its beak open, the third week it silently grows feathers, and on the fourth week, it flies away from the nest. Last week, 20 chicks were sitting with their beaks open, and 14 were growing feathers, while this week, 15 were sitting with their beaks open and 11 were growing feathers. a) How many chicks were sitting with their beaks open two weeks ago? b) How many chicks will be growing feathers next week? In the answer, write the product of these numbers.
Answer: 225

Solution. In fact, the chicks should be divided into three categories: one-week-old, two-week-old, and three-week-old. With each new week, each chick moves to the next category. So, if 11 are feathering this week, then last week there were 11 two-week-olds, and, accordingly, 9 one-week-olds ( $9+11=20$ ). This means that this week there are 9 two-week-olds, and they will be feathering next week. Last week, there were 11 two-week-olds and 14 three-week-olds - which means that the week before last, there were 11 one-week-olds and 14 two-week-olds, and it was they who were opening their beaks. The answer is $9(11+14)$.

## B-2

In a workshop, wooden horses are made. A figurine is painted for two days, on the third day it is lacquered, and on the fourth day, it is shipped to the store. Today, 12 figurines are being painted, and 7 are being lacquered. Yesterday, 11 figurines were painted, and 10 were lacquered. a) How many figurines were painted the day before yesterday? b) How many figurines will be lacquered tomorrow? Write the product of these numbers as the answer.

Answer: 68

## B-3

In an enclosed area of the Universe, stars flare up. Each star shines brightly for two billion years, then glows dimly for a billion years, and then goes out completely. Today, in that area of the Universe, there are 7 bright and 12 dim stars, a billion years ago there were 16 bright and 8 dim. a) How many dim stars will you count there a billion years from now? b) How many bright stars were there two billion years ago? Write the product of the obtained numbers as the answer.

Answer: 80

## B-4

Every year, new models of phones appear on the market. In the first year after release, a model is considered the cutting edge of progress, in the second and third years, the model is downgraded to just "decent," and after that, it hopelessly becomes outdated. This year, there are 8 cutting-edge models and 11 decent ones. Last year, there were 4 cutting-edge models and 17 decent ones. a) How many models were at the cutting edge of progress by the standards of the year before last? b) How many decent models will there be next year? Write the product of the obtained numbers as the answer.

Answer: 84

## Lomonosov Olympiad for Schoolchildren in Mathematics

Preliminary stage $2020 / 21$ academic year for $5-6$ grades

## B-1

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