设x1,x2,x3,x4,x5,x6,x7是自然数,且x1<x2<x3<x4<x5<x6<x7,x1+x2=x3,x2+x3=x4,x3+x4=x5,x4+x5=x6,x5+x6=x7,又x1+x2+x3+x4+x5+x6+x7=2010,

问题描述:

设x1,x2,x3,x4,x5,x6,x7是自然数,且x1<x2<x3<x4<x5<x6<x7,x1+x2=x3,x2+x3=x4,x3+x4=x5,x4+x5=x6,x5+x6=x7,又x1+x2+x3+x4+x5+x6+x7=2010,那么x1+x2+x3的值最大是 ______.

∵x1+x2+x3+x4+x5+x6+x7=13x1+20x2=2010,
利用整除性,x1必是10的奇数倍,又x1<x2
可得

x1=10
x2=94
x1=30
x2=81
x1=50
x2=68
,(x1+x2+x3max=2(x1+x2max=2(50+68)=236.
故答案为:236.