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2014 AMC 10B Problem 24

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2014 AMC 10B Problem 24AMC 10 Step by Step

Name: Date: September 13, 2026

Arrangements with Restrictions · difficulty 4 of 5 · about 8 min · position P21-25

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?

A)
$1$
B)
$2$
C)
$3$
D)
$4$
E)
$5$

2014 AMC 10B Problem 24

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