反对角线 Anti-Diagonal

反对角线是对角线的一种变型。在反对角线内，数字必须尽可能多地在对角线上重复。在九阶反对角线内，每条对角线上含有三种不同数字。

Anti-Diagonal is a variant of Diagonal. In Anti-Diagonal, numbers must repeat as more as they can on each diagonal. In Anti-Diagonal 9x9, each diagonal contains three kinds of numbers.

◆对角线上数字 Numbers on the diagonal

① 如果ABC和DEF都不在对角线上，对角线上必定是GHI。

If ABC and DEF cannot be on the diagonal, numbers on the line must be the GHI.

② 如果A在某宫里不能在对角线上，A也不能在其他宫里在这条对角线上。

If A cannot be in a diagonal in one Box, A cannot be in this diagonal in another Box.

◆互补 Complementariness

通过互补可以形成额外区域。这也是软件生成反对角线的方式之一。

Extra regions exists by complementariness. This is also the way to generate this variant by softwares.

◆特殊数对/组 Special Subsets

练习 Practice

① 九阶反对角线中，如果E5=A，两条对角线上一共有多少个A？

In Anti-Diagonal 9x9, if E5=A, how many times will A appear on the two diagonals?

② 六阶反对角线中，如果A1=A，两条对角线上一共有多少个A？

In Anti-Diagonal 6x6, if A1=A, how many times will A appear on the two diagonals?

③ 解答问号格 Find out the number in ？cells.

答案 Answer

① 5 ② 6 ③ E5=4; F4=9.