#3 Measure Your Calibre

Number Theory Level 4

Check your Calibre


The answer is 111.

Md Zuhair by Md Zuhair , 20, India

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2 solutions

The final single digit number will have same remainder on division with 9 as the original number we start with. This means that we need to find number of positive integers which leave a remainder of 5 on division with 9. This is an AP with 1st term as 5 and last term as 995 and common difference 9..

So 995 = 5 + ( n − 1 ) 9 995=5+(n-1)9 which gives n = 111 n=111

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Did the same way

Nivedit Jain - 4 years, 3 months ago

Nice and neat approach!

Rushikesh Jogdand - 4 years ago
Nivedit Jain
Mar 11, 2017

Another way to solve using multinomial theorem.

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Can you please explain me this theorem for permutations and combinations.. I knoe its usein binomial hut here howcan we do it?

Md Zuhair - 4 years, 3 months ago

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ok. I can send you various articles related to it and my coaching notes if u wish. Are u on facebook then plzz send me friend request i will send you.

Nivedit Jain - 4 years, 3 months ago

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Oksy. Surely.. I will send an fb request... thanks

Md Zuhair - 4 years, 3 months ago

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