Honza set out into the world with a sack of buns. At the first crossroads, he met Long, Wide, and Keen-eyed, and fairly shared his buns with them—each got a quarter of the buns. Honza ate two buns from his share and continued on his way.

At the second crossroads, he met Jeníček and Mařenka, and he shared the remaining buns fairly with them—each got a third of the remaining buns. Honza ate two buns from his share and continued on his way with the rest.

At the third crossroads, he met Snow White. He shared the remaining buns fairly with her, so they both had half of the remaining buns. When Honza ate his two buns again, the sack was empty, and he returned home.

With how many buns did Honza set out into the world?

(M. Petrová)

Hint. How many buns did Honza have when he arrived at the third crossroads?
We can advantageously solve the task from the end:

- At the third crossroads, Honza ate the last 2 buns, which was half of what he brought to this crossroads. Therefore, he came to the third crossroads with 4 buns, and this is also the number with which he left the second crossroads.
- At the second crossroads, he ate 2 buns (and then continued). Before that, he had 6, which was a third of what he brought to this crossroads. Therefore, he came to the second crossroads with 18 buns, and this is also the number with which he left the first crossroads.
- At the first crossroads, he ate 2 buns (and then continued). Before that, he had 20, which was a quarter of what he brought to this crossroads. Therefore, he came to the first crossroads with 80 buns, and this is also the number with which he left home.

Honza set out into the world with 80 buns.

Note. The previous considerations are summarized in the following table:

| crossroads | left | brought |
| :---: | :---: | :---: |
| 3 | 0 | $2 \cdot 2=4$ |
| 2 | 4 | $(4+2) \cdot 3=18$ |
| 1 | 18 | $(18+2) \cdot 4=80$ |