Permutation Adjacent Sum Constraint

1925SpecialistCombinatoricsCounting Principles

AMC 10B · 2012 · Problem 22

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?

Answer choices

120

512

1024

181,440

362,880

0 students attempted0% solvedRating 1925

Related practice paths

AMC 10 PracticeAlgebra, geometry, counting, and number theory practice.AMC 10 vs AMC 12Choose the right practice path and difficulty level.AIME Practice StrategyHow to improve accuracy on high-difficulty problems.

Ready to check your answer?

Create an account to submit answers, save history, and track your rating.

Progressive Hints5

Unlock hints one at a time — each reveals a little more without spoiling the solution.

Step-by-Step Solutions1

Multiple solution approaches with detailed walkthroughs, unlocked after you solve the problem.

AI-Powered Grading

Instant feedback on your answer — handles fractions, decimals, and equivalent forms.

Curated problem bank

Supported tracks for AMC, AIME, MATHCOUNTS, and olympiad-style training, plus global problem sources like UKMT, Euclid, and Kangaroo.