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February 11th, 2013, 10:15 PM   #1
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Coding Theory & Binary Numbers

Am doing questions on Coding theory and binary number system now... couple things have come up...

(Just to clarify, the pics I uploaded below are in the reverse order that I talk about them)

1. A counsellor has 3n+2 campers with her at a juntion in a hiking trail. She knows their camp is ternty minutes down one of four possible paths. It will be dark in one hour and the group must find their camp before dark. n of the 3n+2 campers sometimes lie, and unfortunately the camper doesn't know which n they are.
a) is there a way for the counselor to accurately deduce the location of the camp?
b) prove this problem cannot be solved with only 3n+1 campers.

I attached two pictures to this message showing what I have done so far but don't know where to go from here....

2. (This question is too long to type so I took a picture of it as well)

I feel like I have solved this correctly. Since the number appears on cards 1,3 and 6, the 1st 3rd and 6th digits are 1's. Since the number does not appear on cards 2,4,5, the 2nd 4th and 5th digits are 0's. Therefore the number in binary is 10010 which is equal to 37. Therefore the number is 37.

However... as an extra challenge question he gave us question 3 which which I have uploaded below....
how would the answer to this one be any different... does the whole natural nuber thing in question two make it somehow different from question 3?
Attached Images
 1A - WORK.jpeg (74.1 KB, 430 views) 1B - WORK.jpeg (69.5 KB, 428 views) Question 2.jpeg (93.8 KB, 423 views) CHALLENGE Question 3.png (235.1 KB, 421 views)

 February 11th, 2013, 10:32 PM #2 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Re: Coding Theory & Binary Numbers Are you sure this is a number theory question? I am having a hunch that this post should belong to High school mathematics section . . .
February 11th, 2013, 10:38 PM   #3
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Joined: Jan 2012

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Re: Coding Theory & Binary Numbers

Quote:
 Originally Posted by mathbalarka Are you sure this is a number theory question? I am having a hunch that this post should belong to High school mathematics section . . .
to be honest i had no idea where to put it. The only reason I put it here was because a lot of stuff we do in this class deals with mods, so I assumed the general category of everything was number theory, since there isn't a coding theory section... but since its from a second year uni class I didn't know if I should put it in the high school section haha. If its not right it can be moved...

 February 12th, 2013, 05:47 AM #4 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Coding Theory & Binary Numbers We don't have a good place for coding theory so here is fine. Certainly not high-school material.

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