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MathematicsMathematics
4 June, 00:13

A student at Harvard named Kevin

Was counting his stones by 11

He messed up n times

And instead counted 9s

And wound up at 2007.

To be precise, Kevin divides 2007 stones into groups of 9 stones and 11 stones, where n of the groups have 9 stones in them. How many values of could make this limerick true?

(Kevin can mess up every time)

+3
Answers (1)
  1. 4 June, 00:23
    0
    The answer is 21.

    Work:

    Some groups of 11,

    and some groups of 9,

    together make 2007.

    We may make an equation

    11x + 9y = 2007,

    and we need to find how many possibilities there are for y.

    2007/9=223

    So, the highest value for y is 223.

    Let k be a value for y.

    If k is a valid value for y then (2007-9k) must be divisible by 11.

    Let's just brute force this by doing this validity test with every number from 1 to 223. Then we can count how many valid options there are.

    0 is NOT valid

    1 is valid

    2 is NOT valid

    3 is NOT valid

    4 is NOT valid

    5 is NOT valid

    6 is NOT valid

    7 is NOT valid

    8 is NOT valid

    9 is NOT valid

    10 is NOT valid

    11 is NOT valid

    12 is valid

    13 is NOT valid

    14 is NOT valid

    15 is NOT valid

    16 is NOT valid

    17 is NOT valid

    18 is NOT valid

    19 is NOT valid

    20 is NOT valid

    21 is NOT valid

    22 is NOT valid

    23 is valid

    24 is NOT valid

    25 is NOT valid

    26 is NOT valid

    27 is NOT valid

    28 is NOT valid

    29 is NOT valid

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    34 is valid

    35 is NOT valid

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    42 is NOT valid

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    46 is NOT valid

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    56 is valid

    57 is NOT valid

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    59 is NOT valid

    60 is NOT valid

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    67 is valid

    68 is NOT valid

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    76 is NOT valid

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    78 is valid

    79 is NOT valid

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    89 is valid

    90 is NOT valid

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    92 is NOT valid

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    98 is NOT valid

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    100 is valid

    101 is NOT valid

    102 is NOT valid

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    109 is NOT valid

    110 is NOT valid

    111 is valid

    112 is NOT valid

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    115 is NOT valid

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    117 is NOT valid

    118 is NOT valid

    119 is NOT valid

    120 is NOT valid

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    123 is NOT valid

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    166 is valid

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    178 is NOT valid

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    187 is NOT valid

    188 is valid

    189 is NOT valid

    190 is NOT valid

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    192 is NOT valid

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    194 is NOT valid

    195 is NOT valid

    196 is NOT valid

    197 is NOT valid

    198 is NOT valid

    199 is valid

    200 is NOT valid

    201 is NOT valid

    202 is NOT valid

    203 is NOT valid

    204 is NOT valid

    205 is NOT valid

    206 is NOT valid

    207 is NOT valid

    208 is NOT valid

    209 is NOT valid

    210 is valid

    211 is NOT valid

    212 is NOT valid

    213 is NOT valid

    214 is NOT valid

    215 is NOT valid

    216 is NOT valid

    217 is NOT valid

    218 is NOT valid

    219 is NOT valid

    220 is NOT valid

    221 is valid

    222 is NOT valid

    223 is NOT valid

    21 valid options for y!
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