Difference between revisions of "1999 AIME Problems/Problem 5"
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== Problem == | == Problem == | ||
| + | For any positive integer <math>\displaystyle x_{}</math>, let <math>\displaystyle S(x)</math> be the sum of the digits of <math>\displaystyle x_{}</math>, and let <math>\displaystyle T(x)</math> be <math>\displaystyle |S(x+2)-S(x)|.</math> For example, <math>\displaystyle T(199)=|S(201)-S(199)|=|3-19|=16.</math> How many values <math>\displaystyle T(x)</math> do not exceed 1999? | ||
== Solution == | == Solution == | ||
== See also == | == See also == | ||
| + | * [[1999_AIME_Problems/Problem_4|Previous Problem]] | ||
| + | * [[1999_AIME_Problems/Problem_6|Next Problem]] | ||
* [[1999 AIME Problems]] | * [[1999 AIME Problems]] | ||
Revision as of 00:48, 22 January 2007
Problem
For any positive integer 
, let 
be the sum of the digits of , and let 
be 
For example, 
How many values do not exceed 1999?
