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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?
 +
 +
<math>\text{(A) } 0\quad
 +
\text{(B) } 1\quad
 +
\text{(C) } 2\quad
 +
\text{(D) } 3\quad
 +
\text{(E) } 4</math>
  
 
== Solution ==
 
== Solution ==

Revision as of 15:37, 28 September 2014

Problem

An $n$-digit positive integer is cute if its $n$ digits are an arrangement of the set $\{1,2,...,n\}$ and its first $k$ digits form an integer that is divisible by $k$ , for $k = 1,2,...,n$. For example, $321$ is a cute $3$-digit integer because $1$ divides $3$, $2$ divides $32$, and $3$ divides $321$. Howmany cute $6$-digit integers are there?

$\text{(A) } 0\quad \text{(B) } 1\quad \text{(C) } 2\quad \text{(D) } 3\quad \text{(E) } 4$

Solution

$\fbox{C}$

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

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