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.

Answers:

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?