9.1. Karlson counts 1000 buns baked by Fräulein Bock: «one, two, three, ..., nine hundred ninety eight, nine hundred ninety nine, thousand». How many words will he say in total? (Each word is counted as many times as it was said.)
Answer: 2611.

Solution. One word will be required to pronounce 37 numbers: $1,2,3,4,5,6,7$, $8,9,10,11,12,13,14,15,16,17,18,19,20,30,40,50,60,70,80,90,100,200,300,400$, $500,600,700,800,900,1000$.

Among the first 99 numbers, the number of those pronounced in two words: $99-27=72$, thus, the number of words required for their pronunciation is $2 \cdot 72=144$.

In each subsequent hundred (there are 9 of them), each number that is pronounced in one word in the first hundred will be pronounced in two, and the number of words is $9 \cdot 2 \cdot 27=486$. The rest are pronounced in three words: $9 \cdot 3 \cdot(99-27)=1944$.

Thus, to count all the cookies, $37+144+486+1944=2611$ words will be needed.

## Criteria.

1 point. The number of numbers pronounced in one word is found and justified.

2 points. The number of words required to pronounce numbers from 1 to 99 is found and justified correctly.

2 points. The number of words required to pronounce numbers in any hundred after 100 is found and justified correctly.

Comment. Points for the criteria above are cumulative.

3 points. The correct answer without justification.