# Task 1.

Mom told Dima that he should eat 13 spoons of porridge. Dima told his friend that he had eaten 26 spoons of porridge. Each child, telling about Dima's feat, increased the amount of porridge Dima had eaten by 2 or 3 times. As a result, one of the children told Dima's mom about 33696 spoons of porridge. How many times in total did the children, including Dima, tell about the feat?
Answer: 9

Solution. $33696=2^{5} \cdot 3^{4} \cdot 13$. From this, it follows that the story of the feat was retold 5 times with the amount of porridge doubling and 4 times with it tripling, totaling 9 times.

## B-2

Dad persuaded Natasha to eat 11 spoons of porridge. Natasha told her friend that she had eaten 22 spoons of porridge. Then each child, retelling the story of Natasha's feat, increased the amount of porridge she had eaten by 2 or 3 times. As a result, one of the children told Natasha's dad about 21384 spoons of porridge. How many times in total did the children, including Natasha, retell the story?

## Answer: 8

## B-3

Mom told Grisha that he had to eat 3 spoons of porridge. Grisha told his friend that he had eaten 9 spoons of porridge. Then each child, retelling the story of Grisha's feat, increased the amount of porridge he had eaten by 3 or 5 times. As a result, one of the children told Grisha's mom about 18225 spoons of porridge. How many times in total did the children, including Grisha, retell the story?

Answer: 7

## B-4

Dad persuaded Tanya to eat 7 spoons of porridge. Tanya told her friend that she had eaten 21 spoons of porridge. Then each child, retelling the story of Tanya's feat, increased the amount of porridge she had eaten by 2 or 3 times. As a result, one of the children told Tanya's dad about 27216 spoons of porridge. How many times in total did the children, including Tanya, retell the story?

Answer: 9

## Lomonosov Olympiad for Schoolchildren in Mathematics

Preliminary Stage 2020/21 academic year for 5-6 grades

#