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

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SUMMARY

The discussion centers on determining the missing digit \(X\) in the expression \(9986860883748524X5070273447265625\) which equals \(1995^{10}\). Participants successfully solved the problem, with kaliprasad providing the correct solution. The problem was part of the Problem of the Week (POTW) initiative, encouraging mathematical engagement among forum members. The correct answers were submitted by several users, showcasing collaborative problem-solving.

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

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

Solution from kaliprasad:
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.
 

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