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?
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