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Congrats on finding this page! Here's a problem I made: <math>\newline</math> | Congrats on finding this page! Here's a problem I made: <math>\newline</math> | ||
| − | Suppose a positive integer with all digits non-zero is considered <math>\textit{almost unique}</math> if there are fewer than <math> 5 </math> permutations of its digits. For example, <math> 122 </math> is <math>\textit{almost unique}</math> 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 <math>\textit{almost unique}</math> numbers less than <math> 1000000 </math> are there? | + | Suppose a positive integer with all digits non-zero is considered <math>\textit{almost unique}</math> if there are fewer than <math> 5 </math> permutations of its digits. For example, <math> 122 </math> is <math>\textit{almost unique}</math> 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>, and <math> 321 </math>). How many <math>\textit{almost unique}</math> numbers less than <math> 1000000 </math> are there? |
Revision as of 15:26, 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 
if there are fewer than 
permutations of its digits. For example, 
is since it has 
permutations,(, 
, and 
), while 
is not since it has 
permutations, (, 
, 
, 
, 
, and 
). How many numbers less than 
are there?
