At the "Lukomorye" station, they sell cards for one, five, and twenty rides. All cards cost a whole number of gold coins. Five cards for one ride are more expensive than one card for five rides, and four cards for five rides are more expensive than one card for twenty rides. It turned out that the cheapest way for 33 bogatyrs to travel is to buy cards for 35 rides, spending 33 gold coins on this. How much does a card for five rides cost?
Since 5, 20, and 35 are all divisible by 5, the number of tickets bought for a single ride is also divisible by 5. However, it is more cost-effective to replace every five such tickets with one ticket for five rides. Therefore, there is no need to buy tickets for a single ride. For the same reason, it is most cost-effective to buy three tickets for five rides and one ticket for 20 rides, which costs exactly 33 coins, while seven tickets for five rides cost more. Therefore, a ticket for five rides costs no less than 5 coins.

On the other hand, according to the condition, it is more cost-effective to pay for 35 rides than to buy two tickets for 20 rides, meaning that three tickets for five rides are cheaper than one for 20. Therefore, six tickets for five rides cost less than 33 coins, meaning that one such ticket costs no more than five coins.

## Answer

5 coins.