N和数独 N-Sum

标准数独基础上，提示是这一方向上前若干个数字的和。

Classic rules applied. Additionally, outside clues is the first several numbers' sum.

若干可能意味着1个数字之和，或很多格的和。

Several may means 1, and it can also mean 2,3 or some else number.

◆末端计算 Calculate the end

设行列数字之和为S_n，提示为C_n，设D_n=S_n-C_n，通过D_n的取值，判断不在和之内的数字数量。

Set the whole Row/Column's sum as S_n, and the clue as C_n. Set D_n=S_n-C_n. Use D_n to judge how many numbers do not in the part of sum.

例题中S_n=10，C_n=9，所以D_n=1，不在和之内的数字只能是单个的、位于行列末端的1。

In the example, S_n=10, C_n=9, so D_n=1, numbers do not in the part of sum can only be single 1 at the end of the Row/Column.

◆一些定势 Some patterns

① 提示1或2，必定是1或2在第一格。

Clue 1 and 2 must be 1 or 2 in first cell.

② 提示为M，第一格不大于M。

If the clue is M, the first number cannot be larger than M.

③ 提示M大于阶数N，M至少是两个格的和。

If the clue M is larger than N (in NxN puzzle), then M must be the sum of at least 2 cells.

④ 四阶N和之中，提示6的前三格里必定有2。

In 4x4 N-Sum, clue 6 must contains 2 in first 3 cells.

练习 Practice

① 六阶N和之中，提示是5，第一格可能是______。

In 6x6 N-Sum, a clue is 5, the first number here might be ______.

② 找出问号格内数字 Find out the ？cell.

答案 Answer

① 1~5. ② C2=1.