PSLE Letters C, Y and A formed a patten as shown below.
C Y C A C C Y C A C C Y C A C . . .
If there are 112 'C', what is the greatest possible number of letters in the pattern?
Number of letters in 1 set of C Y C A C = 5
Number of letters 'C' in 1 set of C Y C A C = 3
Number of sets of 3 'C' if there are 112 'C'
= 112 ÷ 3
= 37 r 1
If the remainder is 1, there is 1 'C' and the largest possible number of letters is the final incomplete set is 2. (C Y)
If the remainder is 2, there are 2 'C' and the largest possible number of letters is the final incomplete set is 4. (C Y C A)
Greatest possible number of letters
= 37 x 5 + 2
= 185 + 2
= 187
Answer(s): 187