AMC 10 Step by Step
2012 AMC 10BProblem 22P21-25~6 minPrint

Let (a1,a2,,a10)(a_1,a_2, \dots ,a_{10}) be a list of the first 10 positive integers such that for each 2i102 \le i \le 10 either ai+1a_i+1 or ai1a_i-1 or both appear somewhere before aia_i in the list. How many such lists are there?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.