设一列数a1 a2 a3...a2013中任意四个相邻数之和都是20,已a4=2x,a7=9,a10=1,a100=3x

a1＋a2＋a3＋a4＝a2＋a3＋a4＋a5,a5＋a6＋a7＋a8＝a6＋a7＋a8＋a9,
a9＋a10＋a11＋a12＝a10＋a11＋a12＋a13,a13＋a14＋a15＋a16＝a14＋a15＋a16＋a17,…
∴a1＝a5＝a9＝a13＝a17＝…＝a2013
同理可得：
a2＝a6＝a10＝a14＝a18＝…＝a2010＝1
a3＝a7＝a11＝a15＝a19＝…＝a2011＝9
a4＝a8＝a12＝a16＝a20＝…＝a2012＝3x－1＝2x
∴x＝1,故a4＝2
又a1＋a2＋a3＋a4＝20
∴a1＋1＋9＋2＝20
∴a2013＝a1＝8