Difference between revisions of "2023 AMC 10B Problems/Problem 16"
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| − | == Solution | + | == Solution == |
| − | + | <math>D</math> is greater than <math>U</math> because <math>upno</math> can't start with <math>0</math>. | |
| − | <math>2^9-1 = 511</math>. | + | So the differences are in the form <math>x0</math> |
| + | When x has length <math>k</math> we have <math>{9 \choose k}.</math> | ||
| + | The number of possible <math>x = \sum_{k=1}^9 {9 \choose k} = \sum_{k=0}^9 {9 \choose k} - {9 \choose 0} = 2^9-1 = 511</math>. | ||
~Technodoggo | ~Technodoggo | ||
Revision as of 15:24, 15 November 2023
Solution
is greater than 
because 
can't start with 
.
So the differences are in the form 
When x has length 
we have 
The number of possible 
.
~Technodoggo
