Solution to Puzzle #76: What’s the Final Digit?

I received an overwhelming number of correct responses to this puzzle…though very few from the younger ones. Ones who gave the correct answers included Pooja Goyal, Naresh Kumra, Smiti Mittal, Prakhar Prakash, Girish Tutakne, Ashutosh Diwakar, Aishvarya Gupta, Ashish Gupta, Arushi Gupta and Ishir Gupta. Smiti, Arushi and Ishir deserve a special mention – they are in classes 8th, 9th and 6th respectively.

The answer is 9.

I am taking the liberty of copying the solution from Aishvarya here:

100!(factorial of 100) will always be divisible by  9.

According to the divisibility property of 9, A number is divisible by 9 if the sum of its digits is divisible by 9, 1st iteration’s sum of digits of 100! will be a number divisible by 9.

Applying this property recursively, we can conclude that the final digit will be a multiple of 9. Since we are taking sum till single digit, the final sum has to be 9.

Hope you all enjoyed the puzzle.

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