PSLE Letters Q, H and A formed a patten as shown below.
Q H Q A Q Q H Q A Q Q H Q A Q . . .
If there are 88 'Q', what is the greatest possible number of letters in the pattern?
Number of letters in 1 set of Q H Q A Q = 5
Number of letters 'Q' in 1 set of Q H Q A Q = 3
Number of sets of 3 'Q' if there are 88 'Q'
= 88 ÷ 3
= 29 r 1
If the remainder is 1, there is 1 'Q' and the largest possible number of letters is the final incomplete set is 2. (Q H)
If the remainder is 2, there are 2 'Q' and the largest possible number of letters is the final incomplete set is 4. (Q H Q A)
Greatest possible number of letters
= 29 x 5 + 2
= 145 + 2
= 147
Answer(s): 147