I found this beautiful puzzle on Brilliant.org very recently. A very different kind of puzzle, requires basic knowledge of combinatorics. I have also created a couple of simpler versions so that children can also attempt it.
Original Problem: How many integers between 1 and 1,000,000 have the sum of their digits equal to 18?
Variation 1: How many integers between 1 and 1,000 have the sum of their digits equal to 9?
Variation 2: How many integers between 1 and 1,000 have the sum of their digits equal to 18?
As always, please send your answers directly to me at alokgoyal_2001@yahoo.com. If you like the puzzle, please share it with others. If you have interesting puzzles to share, please send them to me at my e-mail given above.
Happy counting!
Alok Goyal's Puzzles Page 