Just Count: 3,6,9, and so on.

Algebra Level 1

How many digits are there in the number: 23 , 283 , 064 , 365 , 386 , 962 , 890 , 625 23,283,064,365,386,962,890,625 ?

Details and Assumptions

  • You may use the fact the number factors to 5 32 5^{32}

  • You may use the approximation: log 10 5 0.69897 \log_{10} 5 \approx 0.69897


Try this

20 20 23 23 22 22 21 21

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7 solutions

Ashwin Upadhyay
Feb 23, 2015

no. of digits = l o g 5 32 log 5^{32}

=> 32 log 5

=> 22.something..

=>no. of digits=22+1=23

p.s - well there is no harm to verify the answer by counting the digits :p ;)

A concise form to find the no. of digits of a number in base b b can be stated as,

δ ( n ) = log b n + 1 \delta(n)=\left \lfloor \log_bn\right \rfloor +1

where, n n is the number given and δ ( n ) \delta(n) be the function that returns the number of digits of n n when written in base b b .

For this problem, the base is decimal base, so b = 10 b=10 and the given number n = 5 32 n=5^{32}

Prasun Biswas - 6 years, 3 months ago

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link plz try this set

Ashwin Upadhyay - 6 years, 3 months ago

Whoa ......... You blew my MIND !!!!!! AWESOME

Vaibhav Prasad - 6 years, 3 months ago

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link

plz try this set

Ashwin Upadhyay - 6 years, 3 months ago

plz stop kidding

Ashwin Upadhyay - 6 years, 3 months ago

धन्यवाद आपका

Vinay Kumar - 6 years, 3 months ago
Vaibhav Prasad
Feb 23, 2015

On counting gives 23 23

Damn !!!!!!!! This has got to be the most hilarious solution you've ever encountered in your life !!!!! :D

It's really depressing when you even count wrong...

Auden Chase - 6 years, 3 months ago

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XD that would be so sad

somashreee biswas - 6 years, 3 months ago

Did the same thing. :P

Python:

1
print len(str(5**32))

Brock Brown - 6 years, 3 months ago

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EVEN HERE PYTHON !!!!!!!! HAHAHAAHAHAHAHAHAHAHAHAHAHAHAAH

Vaibhav Prasad - 6 years, 3 months ago

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atleast he didn't had to count on his own...

Kislay Raj - 6 years, 3 months ago

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@Kislay Raj THe time it would have taken for him to go to desktop, open python, think and write the code would be the same as the time it would take to count.

P.S. Even i did not count . i too used logarithm , but for fun posted the other thing

Vaibhav Prasad - 6 years, 3 months ago

Lol how about vb6?

MasterPro SX - 6 years, 3 months ago

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Dear God no, please don't make me.

Brock Brown - 6 years, 3 months ago
MasterPro Sx
Mar 4, 2015

Soo.... i'm guessing counting wasn't the correct way to do it? ;-)

Saaket Sharma
Feb 26, 2015

the sum is quite good.....but by writing the whole number in the question ,it's just an eye sight check..that who can read well..

Enrique R.
Mar 6, 2015

I just counted and guessed

Reverse the digits of the exponent, especially if it is a two digit number. 1 to the tenth power has one digit

what about 1 11 1^{11} ?? does it have 11 digits??

Ashwin Upadhyay - 6 years, 3 months ago
Ariel Koiman
Mar 4, 2015

Ceiling(Log10(5^32)) = 23

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