can you please help us solve this maths question?

Question

we wish to make a string of letters which contains every possible three letter combinations of P's and Q's somewhere(that is, it mustcointain all these: PPP,PPQ,PQP,PQQ, QPP, QPQ,QQP and QQQ). An example of such a string,of length 18 is, PPPPQPQQPPQPQQPQQQ
What is the length of the shortest such string?

A:8

B:10

C:12

D:16

E:18

Answer 1

OK, start with PPP. Add Q (getting 4 characters) and you've got PPQ covered. Toss another P on (5, now) and you have PQP covered. We now have:

PPPQP

Toss on a Q, and cover QPQ!

PPPQPQ

Throw on a Q and get PQQ covered, too!

PPPQPQQ

Add a Q; QQQ is done.

Add a P; QQP is covered.

Throw in a P, and QPP is done.

SO,

PPPQPQQQPP is as short as I can manage, off the cuff.

That's 10, B.

NOW, If I'm allowed to connect this into a ring, we can put the QQQ to the PPP and get it down to 8... But THAT is cheating!

I'll go for B.

Answer 2

C: 12

Answer 3

is it C?everyone seems to think its E but you said the length of the SHORTEST string and it can get shorter than 18.it can't be 8 because you cant divide 8 into 3s it cant be 10 because you cant divide it into 3's either but 12/3=4.

Answer 4

Definitely E!

Answer 5

answer= A.8 (solved it on a Microsoft word document)

Answer 6

i would have to guess and say 8
P^3,P^2Q,PQP,PQ^2, QP^2, QPQ, Q^2P,Q^3
but im not sure just a guess

Answer 7

I THINK IT'S C:12

Answer 8

E. that was kind of hard to tell you the truth.

Answer 9

E is the answer

Answer 10

I didn't get the question