Find Last Digit

Number Theory Level 2

9 8 7 6 5 4 3 2 \LARGE 9^{8^{7^{6^{5^{4^{3^{2}}}}}}}

Find the last digit of the number above.


The answer is 1.

Mohd Aasif by Mohd Aasif , 25, India

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1 solution

Achal Jain
Feb 24, 2017

The power can be represented as 9 4 K \large 9^{4K} .

All the number of the form 9 4 k 9^{4k} end with 1.

Hence answer is 1

4 Helpful 0 Interesting 0 Brilliant 0 Confused

yes that was good. but this is not a fair problem(for this site) because brilliant gives you 3 tries to solve it and you can give your answer as 1 or 9 because every power of 9 ends with 1 or 9

Sathvik Acharya - 4 years, 3 months ago

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You are right that every power of 9 9 ends with either 1 or 9, but i have specifically mentioned that the power is of form 4 k 4k and all the power of this form end with 1. hence there is utmost surety that it will end with 1 1

Achal Jain - 4 years, 3 months ago

no what I meant was anyone can get this question right because they could check if it is 9 or 1 because brilliant gives you 3 tries. but your solution explains the answer accurately

Sathvik Acharya - 4 years, 3 months ago

@Achal Jain What a excellent answer friend :-)

Mohd Aasif - 4 years, 3 months ago

that's an excellent solution

Sathvik Acharya - 4 years, 3 months ago

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