Age,carelessbess...But,this time I think I'm right.

來源: 2011-03-17 11:52:50 [舊帖] [給我悄悄話] 本文已被閱讀:

We can draw 26 parallel lines with 4m gap. there 25 spaces.

It's clear that 4m 16m first lost, 8m,12m first won.

Induction: 3(k)+1,first lost,3(k)or 3(k)+2 first won.

let check 3(k+1)+1,

nomatter the Fst plant where, if tree is in gap,Snd near it plant the tree out gap killing 3 gaps,if Fst Put tree out gap ,Snd put the tre in gap killing 3 gaps.

Snd always can let one sid of two trees has 3t gaps (t=0,ok),the other side has (3x+1)

t,x<=k,By induction, one side Fst lost, the other Fst won.So, nomatter Fsd choice which side Fst will be lost.

The proof is for all whole numbers.