I came across this question on a site and I didn't find any solution to this.....(except to use calculator)

The question was

Which digit doesn't occur in the number 2^29 ?

Plz help.....

I came across this question on a site and I didn't find any solution to this.....(except to use calculator)

The question was

Which digit doesn't occur in the number 2^29 ?

Plz help.....

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TopNewestIf 2^29=n (mod 9),then 9-n is the answer. Noticing that 2^3=-1(mod 9),2^29=(2^3)^9x2^2=(-1)^9x2^2=-4=5 (mod 9). Therefore the answer is 9-5=4. This can be easily derived using mod. Hope you got it :) – Krishna Ar · 3 years, 1 month ago

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– Poonayu Sharma · 3 years, 1 month ago

Are there other ways too?Log in to reply

– Krishna Ar · 3 years, 1 month ago

Sorry, I can't fathom any. :(... I'm really bad at intuition :-/Log in to reply

I was trying to solve it using logs etc. . :P

Btw...thanks you sir – Poonayu Sharma · 3 years, 1 month ago

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– Krishna Ar · 3 years, 1 month ago

You're welcome :D....but you're 3 yrs elder, so you must refrain from calling me sir, how could you? And this solution is also inspired by an experiment I did with the cyclicity of digital roots of powers of 2. You could check out my easy-peasy problem on that though :)Log in to reply

– Poonayu Sharma · 3 years, 1 month ago

U deserved "sir" :D.....and I solved the problem u talking about....but not with the (mod 9) method But with cyclic sum of digits of powers of 2Log in to reply

– Krishna Ar · 3 years, 1 month ago

Oh. Well at first ( when I encountered this problem in class 7) I solved this using cyclicity too :)Log in to reply

– Poonayu Sharma · 3 years, 1 month ago

Ohh...well dont u think it becomes a herculean task for a 7 grade guy to do such sums :PLog in to reply

@Poonayu Sharma - Woah! I'm mind -blown!!!! How did you level up in Algebra and Number Theory so soon? What resources did you use to gain here? – Krishna Ar · 3 years ago

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Next target ....JEE ,CALCULUS AND MECHANICS :P – Poonayu Sharma · 3 years ago

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– Krishna Ar · 3 years ago

What did you use to learn all those algebra question- inequalities , Symmetric bounding,,all that. And sorry, I really dont think I can do it faster :(.Log in to reply

.whenever u see a problem. ..try to find a note about it .(That's the only thing I used to crack sums..also me and my 2 friends did few sums together)..I remember daniel liu once gave a link to a note which could be used to solve a problem...It was useful then ..If u don't find any such notes...Google it...believe me problems do become easier then.. :D Hoping ur level soars high :P – Poonayu Sharma · 3 years ago

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– Krishna Ar · 3 years ago

:DLog in to reply

– Poonayu Sharma · 3 years ago

Btw...u planning to do iit? :PLog in to reply

– Krishna Ar · 3 years ago

Nope. I do math only as a hobby. I'd wan't to take up medicine as my mother wants me to do it. U wanna go to IIT or somewhere else Mr. Future Cosmologist?Log in to reply

But the way medical ppl will have a tough competition because of u :P – Poonayu Sharma · 3 years ago

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– Krishna Ar · 3 years ago

Nice :). I also loved the way you ended it with a joke :). You want to become an astronaut or cosmologist? I must say there is a great difference between the two! But, whatever it be I'm sure you'd do well in it :P. You are preparing for IIT on your own? I feel ICSE curriculum is much better than CBSE. What do you feel?Log in to reply

Thanks for ur compliment though ...

And good luck. .. (remember to enjoy life as much as u can now...After 10 ...its hell :( :P) – Poonayu Sharma · 3 years ago

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– Krishna Ar · 3 years ago

YUP. Why do you say life after 10th is hell? In fact, I would consider that heaven. I would have to study only my favorite two subjects. English is passable too. In fact, life now is hell for me!.Log in to reply

but if u manage ur time and other things (which I failed to)...u wont have troubles .. Hope you enjoy it even after school :D – Poonayu Sharma · 3 years ago

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– Krishna Ar · 3 years ago

Oh! Thanks for your well wishes :)Log in to reply

You can view the question here with a detailed solution discussion. – Calvin Lin Staff · 3 years, 1 month ago

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– Nathan Ramesh · 3 years, 1 month ago

Except there you are given that it's a 9 digit number with distinct digits. The first step in this problem is to show that it is a 9 digit number (using log) and then obviously by the way the problem is stated implies that the digits are distinctLog in to reply

– Calvin Lin Staff · 3 years, 1 month ago

That rises an interesting question. Which powers (or 2) are missing exactly 1 digit (but could have repeats of others)? Unfortunately, I don't think there is an easy way to answer this question.Log in to reply

– Poonayu Sharma · 3 years, 1 month ago

Yeah I forgot to mention it because I thought that its understood :PLog in to reply

– Poonayu Sharma · 3 years, 1 month ago

Thank you sir :DLog in to reply