答案是8。称每个“cross”的中心格为“special”的，显然任意“special”的格子不在8*8的边界上。若有 $\ge 9$个“cross”，则由Pigeonhole principle我们知道必有一个被染色的3*3（附件中的图片）中有至少3个“special”的格子，而这显然是不成立的。故至多有8个“cross”。 构造见第一个附件。(I have bad English,so I hope someone can do the translete work )

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yefangzhou wrote: The answer is 8. Consider each of the cross’s centre. It is obvious that none of the centres lie on the boundaries. If there are $\ge 9$ Crosses，From the pigeonhole principle we know there are 3 crosses in a 3 by 3 region (refer to picture), which is obviously impossible. Hence there can only a maximum of 8 crosses. 3(I have bad English,so I hope someone can do the translete work )

Thanks for gghx's translation.