Difference between revisions of "User:Borealbear"

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Congrats on finding this page! Here's a problem I made:
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Congrats on finding this page! Here's a problem I made: \\
Suppose a positive integer with all digits non-zero is considered [i]almost unique[/i] if there are fewer than <math> 5 </math> permutations of its digits. For example, <math> 122 </math> is [i]almost unique[/i] since it has <math> 3 </math> permutations,(<math> 122 </math>, <math> 212 </math>, and <math> 221 </math>), while <math> 123 </math> is not since it has <math> 6 </math> permutations, (<math>123</math>, <math> 132 </math>, <math> 213 </math>, <math> 231 </math>, <math> 312 </math>, <math> 321 </math>). How many [i]almost unique[/i] numbers less than <math> 1000000 </math> are there?
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Suppose a positive integer with all digits non-zero is considered \textit{almost unique} if there are fewer than <math> 5 </math> permutations of its digits. For example, <math> 122 </math> is [i]almost unique[/i] since it has <math> 3 </math> permutations,(<math> 122 </math>, <math> 212 </math>, and <math> 221 </math>), while <math> 123 </math> is not since it has <math> 6 </math> permutations, (<math>123</math>, <math> 132 </math>, <math> 213 </math>, <math> 231 </math>, <math> 312 </math>, <math> 321 </math>). How many \textit{almost unique} numbers less than <math> 1000000 </math> are there?

Revision as of 16:24, 22 April 2021

AIME Qual


























Congrats on finding this page! Here's a problem I made: \\ Suppose a positive integer with all digits non-zero is considered \textit{almost unique} if there are fewer than $5$ permutations of its digits. For example, $122$ is [i]almost unique[/i] since it has $3$ permutations,($122$, $212$, and $221$), while $123$ is not since it has $6$ permutations, ($123$, $132$, $213$, $231$, $312$, $321$). How many \textit{almost unique} numbers less than $1000000$ are there?

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