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        riddles >> easy >> 7^1000
        
(Message started by: codpro880 on Feb 26^th, 2009, 11:44am)

Title: 7^1000
Post by codpro880 on Feb 26^th, 2009, 11:44am

What is the number in the units place in 7^1000? Why?

Title: Re: 7^1000
Post by pex on Feb 26^th, 2009, 12:03pm

Well, [hide]7⁴ = 1 (mod 10)[/hide], so 7¹⁰⁰⁰ [hide]= 1²⁵⁰ = 1 (mod 10)[/hide], right?

Title: Re: 7^1000
Post by towr on Feb 26^th, 2009, 12:04pm

A similar thread: http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_easy;action=display;num=1210461451

Title: Re: 7^1000
Post by codpro880 on Feb 26^th, 2009, 5:31pm

Yes, 1 is the correct answer. I don't understand the mod stuff though :/. I need more schooling.

The way I solved the problem was by noticing that the powers of seven repeat the digits in the unit place in a pattern.
7^1=7
7^2=49
7^3=343
7^4=2401
7^5=16807
7^6=117649
etc.

Title: Re: 7^1000
Post by pex on Feb 26^th, 2009, 10:51pm

on 02/26/09 at 17:31:35, codpro880 wrote:

I don't understand the mod stuff though :/

http://en.wikipedia.org/wiki/Modular_arithmetic is a good place to start. (Please note that officially, I used the "=" sign inappropriately; it should be something like "=".)

Title: Re: 7^1000
Post by Hippo on Mar 2^nd, 2009, 8:10am

on 02/26/09 at 22:51:16, pex wrote:

I used the "=" sign inappropriately; it should be something like "=".)

http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/equiv.gif

Title: Re: 7^1000
Post by codpro880 on Mar 2^nd, 2009, 11:08am

So it's kind of like using different number bases except you go in a circle?

Title: Re: 7^1000
Post by towr on Mar 2^nd, 2009, 11:31am

on 03/02/09 at 11:08:12, codpro880 wrote:

So it's kind of like using different number bases except you go in a circle?

Yes, that's a good way to look at it.
Just like using a clock, also. Add 24 hours and you get the same time again.

Title: Re: 7^1000
Post by codpro880 on Mar 2^nd, 2009, 3:53pm

on 02/26/09 at 12:03:44, pex wrote:

Well, [hide]7⁴ = 1 (mod 10)[/hide], so 7¹⁰⁰⁰ [hide]= 1²⁵⁰ = 1 (mod 10)[/hide], right?

I still don't get pex's logic ???

Title: Re: 7^1000
Post by River Phoenix on Mar 2^nd, 2009, 5:16pm

on 03/02/09 at 15:53:52, codpro880 wrote:

I still don't get pex's logic ???

multiplication still works in a modulus number system, it just loops around.
so since 7^4 = 1 (mod 10), therefore 7^8 = 1 * 1 = 1 (mod 10), etc.