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 :)

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Are there other ways too?

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

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Ohh...use of mod didn't strike me :P

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

Btw...thanks you sir

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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 :)

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@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?

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Next target ....JEE ,CALCULUS AND MECHANICS :P

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.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

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But the way medical ppl will have a tough competition because of u :P

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Thanks for ur compliment though ...

And good luck. .. (remember to enjoy life as much as u can now...After 10 ...its hell :( :P)

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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

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You can view the question here with a detailed solution discussion.

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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 distinct

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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.

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Yeah I forgot to mention it because I thought that its understood :P

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Thank you sir :D

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