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Math

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How many ordered pairs of natural numbers (n, m) are there that solve the equation
2n + 3m = 100

  • Math -

    Well we could argue about if zero counts as a natural number. If it does then


    2n will always be zero or even

    2 n = 0 2 4 6 8 ...... 50 ....100

    3 m is zero or a multiple of 3

    3 m = 0 3 6 9 12 15 ....33 .... 99

    now the sum of those must be 100, which is even so delete all the odd 3ms

    3 m = 0 6 12 18 24 .... 90 96

    now which could add to 100
    4 + 96
    10 + 90
    16 + 84
    22 + 78
    28 + 72 add six, subtract 6, see pattern
    34 + 66
    40 + 60
    46 + 54
    52 + 48
    58 + 42
    64 + 36
    70 + 30
    76 + 24
    82 + 18
    88 + 12
    94 + 6
    100 + 0 count them :)

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