PSLE Letters M, S and Y formed a patten as shown below.
M S M Y M M S M Y M M S M Y M . . .
If there are 109 'M', what is the greatest possible number of letters in the pattern?
Number of letters in 1 set of M S M Y M = 5
Number of letters 'M' in 1 set of M S M Y M = 3
Number of sets of 3 'M' if there are 109 'M'
= 109 ÷ 3
= 36 r 1
If the remainder is 1, there is 1 'M' and the largest possible number of letters is the final incomplete set is 2. (M S)
If the remainder is 2, there are 2 'M' and the largest possible number of letters is the final incomplete set is 4. (M S M Y)
Greatest possible number of letters
= 36 x 5 + 2
= 180 + 2
= 182
Answer(s): 182