Difference between revisions of "1991 AHSME Problems/Problem 26"
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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? | ||
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| + | == Solution == | ||
| + | <math>\fbox{}</math> | ||
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| + | == See also == | ||
| + | {{AHSME box|year=1991|num-b=25|num-a=27}} | ||
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| + | [[Category: Intermediate Number Theory Problems]] | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 01:58, 28 September 2014
Problem
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?
Solution
See also
| 1991 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 25 |
Followed by Problem 27 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
