A student at Harvard named Kevin Was counting his stones by 11 He messed up n times And instead counted 9s And wound

Question

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)

in progress 0
Ximena 2 weeks 2021-09-15T02:22:25+00:00 1 Answer 0

Answers ( )

    0
    2021-09-15T02:23:45+00:00

    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
    30 is NOT valid
    31 is NOT valid
    32 is NOT valid
    33 is NOT valid
    34 is valid
    35 is NOT valid
    36 is NOT valid
    37 is NOT valid
    38 is NOT valid
    39 is NOT valid
    40 is NOT valid
    41 is NOT valid
    42 is NOT valid
    43 is NOT valid
    44 is NOT valid
    45 is valid
    46 is NOT valid
    47 is NOT valid
    48 is NOT valid
    49 is NOT valid
    50 is NOT valid
    51 is NOT valid
    52 is NOT valid
    53 is NOT valid
    54 is NOT valid
    55 is NOT valid
    56 is valid
    57 is NOT valid
    58 is NOT valid
    59 is NOT valid
    60 is NOT valid
    61 is NOT valid
    62 is NOT valid
    63 is NOT valid
    64 is NOT valid
    65 is NOT valid
    66 is NOT valid
    67 is valid
    68 is NOT valid
    69 is NOT valid
    70 is NOT valid
    71 is NOT valid
    72 is NOT valid
    73 is NOT valid
    74 is NOT valid
    75 is NOT valid
    76 is NOT valid
    77 is NOT valid
    78 is valid
    79 is NOT valid
    80 is NOT valid
    81 is NOT valid
    82 is NOT valid
    83 is NOT valid
    84 is NOT valid
    85 is NOT valid
    86 is NOT valid
    87 is NOT valid
    88 is NOT valid
    89 is valid
    90 is NOT valid
    91 is NOT valid
    92 is NOT valid
    93 is NOT valid
    94 is NOT valid
    95 is NOT valid
    96 is NOT valid
    97 is NOT valid
    98 is NOT valid
    99 is NOT valid
    100 is valid
    101 is NOT valid
    102 is NOT valid
    103 is NOT valid
    104 is NOT valid
    105 is NOT valid
    106 is NOT valid
    107 is NOT valid
    108 is NOT valid
    109 is NOT valid
    110 is NOT valid
    111 is valid
    112 is NOT valid
    113 is NOT valid
    114 is NOT valid
    115 is NOT valid
    116 is NOT valid
    117 is NOT valid
    118 is NOT valid
    119 is NOT valid
    120 is NOT valid
    121 is NOT valid
    122 is valid
    123 is NOT valid
    124 is NOT valid
    125 is NOT valid
    126 is NOT valid
    127 is NOT valid
    128 is NOT valid
    129 is NOT valid
    130 is NOT valid
    131 is NOT valid
    132 is NOT valid
    133 is valid
    134 is NOT valid
    135 is NOT valid
    136 is NOT valid
    137 is NOT valid
    138 is NOT valid
    139 is NOT valid
    140 is NOT valid
    141 is NOT valid
    142 is NOT valid
    143 is NOT valid
    144 is valid
    145 is NOT valid
    146 is NOT valid
    147 is NOT valid
    148 is NOT valid
    149 is NOT valid
    150 is NOT valid
    151 is NOT valid
    152 is NOT valid
    153 is NOT valid
    154 is NOT valid
    155 is valid
    156 is NOT valid
    157 is NOT valid
    158 is NOT valid
    159 is NOT valid
    160 is NOT valid
    161 is NOT valid
    162 is NOT valid
    163 is NOT valid
    164 is NOT valid
    165 is NOT valid
    166 is valid
    167 is NOT valid
    168 is NOT valid
    169 is NOT valid
    170 is NOT valid
    171 is NOT valid
    172 is NOT valid
    173 is NOT valid
    174 is NOT valid
    175 is NOT valid
    176 is NOT valid
    177 is valid
    178 is NOT valid
    179 is NOT valid
    180 is NOT valid
    181 is NOT valid
    182 is NOT valid
    183 is NOT valid
    184 is NOT valid
    185 is NOT valid
    186 is NOT valid
    187 is NOT valid
    188 is valid
    189 is NOT valid
    190 is NOT valid
    191 is NOT valid
    192 is NOT valid
    193 is NOT valid
    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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