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24/7(四合一)

Twenty Four Seven (Four-in-One)

专题
Discrete Math / 离散数学
难度
L6

题目详情

这是四合一的 Twenty Four Seven 网格题。四个网格被合并在一个 12×12 大网格中,需要同时满足每个子网格规则,完成后根据空白区域面积计算最终答案。

英文原题

Four Twenty Four Seven grids have been smooshified together within the 12-by-12 grid above.

Place numbers in some of the empty cells so that in total each of the four 7-by-7 outlined grids is a legal “Twenty Four Seven” grid. Namely: each 7-by-7 grid’s interior should contain one 1, two 2’s, etc., up to seven 7’s. Furthermore, each row and column within the 7-by-7’s must contain exactly 4 numbers which sum to 20. Finally, the numbered cells must form a connected region, but every 2-by-2 subsquare in the completed grid must contain at least one empty cell.

Some numbers have been placed inside the grid. Additionally, some blue numbers have been placed outside the grid. A number outside the grid represents either the sum of the row or column it is facing, or the value of the first number it sees in that row or column.

Once completed, you can submit as your answer the product of the areas of the connected groups of orthogonally adjacent empty squares in the grid.

解析

题目是四个相互重叠的 Twenty Four Seven 网格合并成一个大网格。完成网格后,所有大小大于 1 的空白区域面积依次为 5,3,5,8,6,4,4,9,6,3,4,25,3,5,8,6,4,4,9,6,3,4,2,它们的乘积为 74,649,60074,649,600,即最终答案。


英文解析

For February’s puzzle, you were asked to solve four overlapping “Twenty Four Seven” grids smooshified into one big puzzle. Pictured above is the fully completed grid. The empty regions of size greater than 1 have sizes 5, 3, 5, 8, 6, 4, 4, 9, 6, 3, 4, and 2, which multiply to 74,649,600.

Congrats to those of you who successfully completed the grid!