# Homework Help: Pigenhole principle

1. Aug 20, 2011

### AkilMAI

Let T={0,1,2} so that T^11 represents the set of all strings of eleven digits of T.
a)for every T=T_1T_2...T_11 show that there is a pair T_iT_i+1 of consecutive digits that is repeated using the pigenhole principle.
b)Find a string from T of 10 digits where no repetition exists.
c)Find with justification a postive integer N such that every string of N digits of T contains a repeated triple T_iT_i+1T_i+2.

a)Since there are 9 possible pairs and 11 digits one pair will be contained at least once in the string.Is this correct?
b)0011220102.
c)I don't know.How should I proceed?

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2. Aug 20, 2011

### vela

Staff Emeritus
Yeah, that's right.
Try again!
Think about why you can write a 10-digit number with no pairs repeating but not an 11-digit number. How would you generalize this to the case of triples?

3. Aug 21, 2011

### AkilMAI

b)2001022112
c)There are 27 different triples
a string of n digist must have n-2 triples in it,we are substracting the last 2 digits.
So 28+2=30 will work.(or I could just look in terms of 27+another triple(3)=30)

4. Aug 21, 2011

### vela

Staff Emeritus
Good job!