MATH
posted by wan .
A SCHOOL IS DIVIDED INTO 4 HOUSES P,Q,R,S. ON SPORTS DAY,STUDENTS LINE UP SO THAT A STUDENT FROM P IS FIRST IN LINE,THEN A STUDENT FROM Q THEN A STUDENT FROM R THEN A STUDENT FROM S THEN A STUDENT FROM P AND SO ON WITH SAME ORDER REPEATING .FROM WHAT HOUSE WILL THE 66TH STUDENT COME? PLEAE EXPLAIN HOW OU WORK IT OUT,THANKS

House P has students numbers
1 5 9 13 17 ........ (4n3)
House Q has students numbers
2 6 10 14 ...... (4n2)
etc
4n3 = 66
4n = 69 > no whole number solution
4n2 = 66
4n = 68
n = 17  Yeah
The 66th student is in house Q
or
make 4 columns
P...Q...R....S
1 .. 2 .. 2 .. 4
5 .. 6 .. 7 .. 8
9 .. 10 11 12
13 14 15 16
17 18 19 20
...
65 66 67 68
for P  remainder of 1 when divided by 4
for Q  remainder of 2 when divided by 4  66
for R  remainder of 3 when divided by 4