[ Inequalities. Case Analysis ] [ Numerical Inequalities. Comparing Numbers. ]

Nine identical sparrows peck at fewer than 1001 grains, while ten such sparrows peck at more than 1100 grains. How many grains does each sparrow peck?

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Notice, a sparrow can peck only an integer number of seeds.

## Solution

Since 10 sparrows peck more than 1100 seeds, then 9 sparrows will peck more than (1100 : 10) $9=990$ seeds. At the same time, it is known that 9 sparrows peck fewer than 1001 seeds. The only number divisible by 9 in the range from 991 to 1000 is 999. Therefore, 9 sparrows peck 999 seeds, and 1 sparrow pecks 111 seeds.

## Answer

111 seeds.