Difference between revisions of "2014 AMC 10B Problems/Problem 24"

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==Problem==<math>
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==Problem==
The numbers 1, 2, 3, 4, 5 are to be arranged in a circle. An arrangement is </math>bad<math> if it is not true that for every </math>n<math> from </math>1<math> to </math>15<math> one can find a subset of the numbers that appear consecutively on the circle that sum to </math>n<math>. Arrangements that differ only by a rotation or a reflection are considered the same. How many different bad arrangements are there?
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The numbers 1, 2, 3, 4, 5 are to be arranged in a circle. An arrangement is <math>bad</math> if it is not true that for every <math>n</math> from <math>1</math> to <math>15</math> one can find a subset of the numbers that appear consecutively on the circle that sum to <math>n</math>. Arrangements that differ only by a rotation or a reflection are considered the same. How many different bad arrangements are there?
  
</math> \textbf {(A) } 1 \qquad \textbf {(B) } 2 \qquad \textbf {(C) } 3 \qquad \textbf {(D) } 4 \qquad \textbf {(E) } 5 $
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<math> \textbf {(A) } 1 \qquad \textbf {(B) } 2 \qquad \textbf {(C) } 3 \qquad \textbf {(D) } 4 \qquad \textbf {(E) } 5 </math>
  
 
==Solution==
 
==Solution==

Revision as of 15:48, 20 February 2014

Problem

The numbers 1, 2, 3, 4, 5 are to be arranged in a circle. An arrangement is $bad$ if it is not true that for every $n$ from $1$ to $15$ one can find a subset of the numbers that appear consecutively on the circle that sum to $n$. Arrangements that differ only by a rotation or a reflection are considered the same. How many different bad arrangements are there?

$\textbf {(A) } 1 \qquad \textbf {(B) } 2 \qquad \textbf {(C) } 3 \qquad \textbf {(D) } 4 \qquad \textbf {(E) } 5$

Solution

See Also

2014 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 23
Followed by
Problem 25
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
All AMC 10 Problems and Solutions

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