What eight coins should be taken so that with their help, any amount from 1 kopek to 1 ruble can be paid without change?

(Coins in circulation were 1, 3, 5, 10, 20, and 50 kopeks.)
Try to break this task into two: first, find the coins with which you can pay any amount from 1 to 10 kopecks, then - the coins with which you can pay 10, 20, ..., 90 kopecks.

## Solution

Let's take coins of denominations $1,1,3,5,10,10,20,50$ kopecks. It is not difficult to verify that the first four coins allow you to pay any amount from 1 to 9 kopecks, and the last four - any multiple of 10 amount from 10 to 100 kopecks. Therefore, with the specified set of coins, you can pay any amount from 1 kopeck to 100 kopecks.

## Answer

$1,1,3,5,10,10,20,50$ kopecks.