Difference between revisions of "AoPS Wiki talk:Problem of the Day/June 15, 2011"
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==Solution== | ==Solution== | ||
| − | { | + | We can solve this problem by a bit of trial and error. We can guess she rode <math>5</math> days and we get <math>7+10+13+16+19=(13)(5)=65</math> since the mean is clearly <math>13</math> and there are <math>5</math> terms. That's a bit too small. We can add <math>22</math> to <math>65</math> and get <math>87</math>. That's still to small. Now, we add <math>25</math> to get <math>112</math>, the answer we want. We now count how many numbers are in the following list: <math>7, 10, 13, 16, 19, 22, 25</math>. Adding <math>2</math> to the list gives us <math>9, 12, 15, 18, 21, 24, 27</math>. Dividing by <math>3</math> gives us <math>3, 4, 5, 6, 7, 8, 9</math>. Subtracting <math>2</math> gives us <math>1, 2, 3, 4, 5, 6, 7</math>. Our list has <math>7</math> numbers. Since she started on a Monday, we must add <math>6</math> days. Our answer is <math>\boxed{Sunday}</math> |
Revision as of 20:44, 14 June 2011
Problem
AoPSWiki:Problem of the Day/June 15, 2011
Solution
We can solve this problem by a bit of trial and error. We can guess she rode 
days and we get 
since the mean is clearly 
and there are terms. That's a bit too small. We can add 
to 
and get 
. That's still to small. Now, we add 
to get 
, the answer we want. We now count how many numbers are in the following list: 
. Adding 
to the list gives us 
. Dividing by 
gives us 
. Subtracting gives us 
. Our list has 
numbers. Since she started on a Monday, we must add 
days. Our answer is 
