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MATH

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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

  • MATH -

    House P has students numbers
    1 5 9 13 17 ........ (4n-3)
    House Q has students numbers
    2 6 10 14 ...... (4n-2)
    etc

    4n-3 = 66
    4n = 69 --> no whole number solution

    4n-2 = 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

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