Galperin G.A.

Two sums are written on the board:

$1+22+333+4444+55555+666666+7777777+88888888+999999999$

$9+98+987+9876+98765+987654+9876543+98765432+987654321$

Determine which of them is greater (or if they are equal).
Let's write both sums in column form, and for better clarity, the second one in reverse order. In both sums, the digits from 1 to 9 will be added in the units place, the digits from 2 to 9 in the tens place, the digits from 3 to 9 in the hundreds place, and so on. The digit obtained in each place and the carry to the higher place will be the same in both cases. Therefore, the result of the addition will be the same.
![](https://cdn.mathpix.com/cropped/2024_05_06_46af0608f2d2cb90d801g-03.jpg?height=632&width=1072&top_left_y=1502&top_left_x=116)

Of course, both sums can be calculated directly, resulting in 1097393685. But this is a rather laborious and uninteresting way.

## Answer

They are equal.

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