设x¹x²x³x4x5x6x7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＝20

Question

设x¹x²x³x4x5x6x7是自然数,且x¹＜x²＜x³＜x4＜x5＜x6＜x7,x¹＋x²＝x ³,x ²＋x ³＝x4,x ³＋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＿.

Answer 1

x 3=x1＋x2
x4＝x 2＋x 3=x1＋2x2
x5=x 3＋x4=2x1＋3x2
x6=x4＋x5=3x1＋5x2
x7=x5＋x6=5x1＋8x2
x1＋x2＋x3＋x4＋x5＋x6＋x7=13x1＋20x2=2010
x1x2是自然数2010-13x1要能被20整除,且x1＜x2
x1=10,30,50
x2=94,81,68
x1＋x2最大值50+68=118
x1＋x2＋x3最大值=118+118=236