A beautiful puzzle for ages 10-100! Found this in Mathematical Circle Diaries, Year 1 (for grade 5-7), Session 25, problem #8.

Robby the Robot multiplied the numbers from 1 to 100 (100 factorial) and calculated the sum of the digits of this product. For this sum, Robby calculated the sum of its digits as well. The robot kept repeating this operation till he got a one-digit number. What was the number?

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 crunching!