Thanks to LP for sharing the concept.

The next time will be January 01, 2101.

This is the 252 day of the year. The sum of those digits equals 9 (2+5+2)

Multiply 9 by any other single-digit number, and then look at the product. The sum of the two digits will equal 9.

**REALLY?**I don't think so. But let's try it.

9 x 1 = 9 ( 9 = 9)

9 x 2 = 18 (1 + 8 = 9)

9 x 3 = 27 ( 2 + 7 = 9)

9 x 4 = 36 ( 3 + 6 = 9)

9 x 5 = 45 ( 4 + 5 = 9)

9 x 6 = 54 ( 5 + 4 = 9)

9 x 7 = 63 ( 6 + 3 = 9)

9 x 8 = 72 ( 7 + 2 = 9)

9 x 9 = 81 ( 8 + 1 = 9)

**Multiply 9 by any two or three-digit number, and then look at the product.**

**The sum of the digits will equal 9 or multiples of 9.**

9 x 15 = 135 ( 1 + 3 + 5 = 9)

9 x 46 = 414 ( 4 + 1 + 4 = 9)

9 x 77 = 693 ( 6 + 9 + 3 = 18 and we find that 1+ 8 = 9)

9 x 864 = 7776 ( 7 + 7 + 7 + 6 = 27 and 2 + 7 = 9)

**Wow!**

**Let's try a 4-digit number**

9 x 2009 = 18081 you can already see this is going to work! (1 + 8 + 8 + 1 = 18 and 1 + 8 = 9)

**OK, now a 5-digit number**

9 x 12525 = 112725 = ( 1 + 1 + 2 + 7 + 2 + 5 = 18 and 1 + 8 = 9)

**How about a 6-digit number?**

9 x 654987 = 5,894,883 = ( 5 + 8 + 9 + 4 + 8 + 8 + 3)

Can we simplify the process? Look at digits in the product.

We have one 9 standing on its own.

If we add the 5 and the 4 we get 9.

We have a 3 and three 8s left.

Let's split the 3 into ones and add them to each of the 8s. We have 3 more 9s now.

**Let's use this on a 7-digit number**

9 x 1234567 = 11111103 = 9

**Will it work on an 8-digit number?**

9 x 22446688 = 202020192 (4 2s and a 1 + 9)

**Finally, will this same scheme still**

**work on an 9-digit number?**

9 x 555888222 = 5002993998 (5 + 2 + 3 + 8 = 18 and 4 nines)

**YES!!**

No, I can't quite explain the theory on this ... I'm a publisher, not a mathematician!

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