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2012 AMC 10B Problem 22

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2012 AMC 10B Problem 22AMC 10 Step by Step

Name: Date: September 13, 2026

Arrangements with Restrictions · difficulty 4 of 5 · about 6 min · position P21-25

Let $(a_1,a_2, \dots ,a_{10})$ be a list of the first 10 positive integers such that for each $2 \le i \le 10$ either $a_i+1$ or $a_i-1$ or both appear somewhere before $a_i$ in the list. How many such lists are there?

A)
$120$
B)
$512$
C)
$1024$
D)
$181,440$
E)
$362,880$

2012 AMC 10B Problem 22

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