MHB What Is the Missing Digit in \(1995^{10}\)?

[anemone]

Here is this week's POTW:

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Find the digit $X$ such that $9986860883748524X5070273447265625$ equals $1995^{10}$.

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Remember to read the https://mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to https://mathhelpboards.com/forms.php?do=form&fid=2!

 

[anemone]

Congratulations to the following members for their correct solution!(Cool)

1. kaliprasad
2. castor28
3. Olinguito
4. greg1313
5. lfdahl

Solution from kaliprasad:

Spoiler

Because 1995 is divisible by 3 so all the powers $\ge 2$ of 1995 shall be divisible by 9.
So sum of digits of the result must be divisible by 9.
We get sum of digits of given number = 160 + X.
Smallest multiple of 9 above 160 is 162 which gives X= 2 and next multiple of 9 gives x = 11. So X= 2 is the right answer.