[GOPJ]

111,111,111 x 111,111,111 = 12,345,678,987, 654,321

Weird.

[Fresh Wind]

Weirder still:

[Dutch Boy]

This works for any number up to 9 digits that are all 1s

11
x11

---

11
+110

=121

11 x 11 = 121
111 x 111 = 12,321
1,111 x 1,111 = 1,234,321
11,111 x 11,111 123,454,321
111,111 x 111,111 = 12,345,654,321
1,111,111 x 1,111,111 = 1,234,567,654,321
11,111,111 x 11,111,111 = 1,234,567,654,321
111,111,111 x 111,111,111 = 12,345,678,987,654,321

Once you get to ten ones, the pattern falls apart.
1,111,111,111 x 1,111,111,111 = 1234567900987650000

Numbers can do strange things under the right conditions.

[Aevery_Freeman]

No, Pascal's triangle.

11x11=121, 111x111=12321...