Difference between revisions of "1985 AIME Problems/Problem 8"
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== Problem == | == Problem == | ||
| − | + | The sum of the following seven numbers is exactly 19: <math>a_1 = 2.56</math>, <math>a_2 = 2.61</math>, <math>a_3 = 2.65</math>, <math>a_4 = 2.71</math>, <math>a_5 = 2.79</math>, <math>a_6 = 2.81</math>, <math>a_7 = 2.86</math>. It is desired to replace each <math>a_i</math> by an [[integer]] approximation <math>A_i</math>, <math>1\le i \le 7</math>, so that the sum of the <math>A_i</math>'s is also 19 and so that <math>M</math>, the [[maximum]] of the "errors" <math>\| A_i-a_i\|</math>, the maximum [[absolute value]] of the difference, is as small as possible. For this minimum <math>M</math>, what is <math>100M</math>? | |
== Solution == | == Solution == | ||
| − | + | {{solution}} | |
== See also == | == See also == | ||
| + | * [[1985 AIME Problems/Problem 7 | Previous problem]] | ||
| + | * [[1985 AIME Problems/Problem 9 | Next problem]] | ||
* [[1985 AIME Problems]] | * [[1985 AIME Problems]] | ||
Revision as of 15:30, 19 November 2006
Problem
The sum of the following seven numbers is exactly 19: 
, 
, 
, 
, 
, 
, 
. It is desired to replace each 
by an integer approximation 
, 
, so that the sum of the 's is also 19 and so that 
, the maximum of the "errors" 
, the maximum absolute value of the difference, is as small as possible. For this minimum , what is 
?
Solution
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