Difference between revisions of "1991 AHSME Problems/Problem 26"
(Created page with "An <math>n</math>-digit positive integer is cute if its <math>n</math> digits are an arrangement of the set <math>\{1,2,...,n\}</math> and its first <math>k</math> digits form a...") |
|||
| Line 1: | Line 1: | ||
An <math>n</math>-digit positive integer is cute if its <math>n</math> digits are an arrangement of the set <math>\{1,2,...,n\}</math> and its first | An <math>n</math>-digit positive integer is cute if its <math>n</math> digits are an arrangement of the set <math>\{1,2,...,n\}</math> and its first | ||
<math>k</math> digits form an integer that is divisible by <math>k</math> , for <math>k = 1,2,...,n</math>. For example, <math>321</math> is a cute <math>3</math>-digit integer because <math>1</math> divides <math>3</math>, <math>2</math> divides <math>32</math>, and <math>3</math> divides <math>321</math>. Howmany cute <math>6</math>-digit integers are there? | <math>k</math> digits form an integer that is divisible by <math>k</math> , for <math>k = 1,2,...,n</math>. For example, <math>321</math> is a cute <math>3</math>-digit integer because <math>1</math> divides <math>3</math>, <math>2</math> divides <math>32</math>, and <math>3</math> divides <math>321</math>. Howmany cute <math>6</math>-digit integers are there? | ||
| + | {{MAA Notice}} | ||
Revision as of 13:54, 5 July 2013
An 
-digit positive integer is cute if its digits are an arrangement of the set 
and its first
digits form an integer that is divisible by , for 
. For example, 
is a cute 
-digit integer because 
divides , 
divides 
, and divides . Howmany cute 
-digit integers are there?
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
