Math Is Fun Forum

Hi all

I was playing around with numbers when I noticed a fun little pattern involving numbers ending in 9.

So the numbers 19, 29, 39, 49.... 99 are equal to the sum of their digits plus the product of their digits. An example: 19 = (1*9) + (1+9), and 99 = (9*9) + (9+9).

You can take this a step further to include 109 119 and so on, by doing the following: 109 = (10*9) + (10+9).

I generalized this form to be: 10a + b = ab + (a + b). Which nicely reduces into b = 9, explaining why this only occurs for digits ending in 9. You can also include just "9" in this pattern, assuming you allow a = 0.

Nothing really more than that, just thought it was fun and I couldn't find this online, but I imagine I just didn't search for the right stuff.