[理工] [離散] 請問一題鴿籠
Let x1,x2...x20 為整數, x1,x2...x20≧1 x1+x2+...+x20 = 30
(a)Show that there exist i and j such that i≦j and xi+....+xj = 9
(b)Show that there exist i and j such that i≦j and xi+....+xj = 10
有問題的是第二小題
我假設s1 = x1;
s2 = x1+x2;
s3 = x1+x2+x3;
以此類推
然後1≦s1<s2....<s20≦30
之後列出s1,s2,....s20,s1+9,s2+9,...s20+9≦39 得證
但是第二小題卻剛好都是40個
請問該怎麼解呢
ps. 99高大
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