Magic Multiplications with Digits

example

1

2

3

4

5

6

7

8

9

10

11

12

13

number of products

5

9×9=81

99×99=9801

999×999=998001

9999×9999=99980001

99999×99999=9999800001

See some patterns generated by arithmetic involving numbers whose digits increase, decrease, or are repeated, or by multiples of some digit. Try to figure out why these curious patterns appear.