by Henry Kwok

### The Rules of "Intersection Sums Sudoku"

Like the standard Sudoku, this Sudoku variant consists of a grid of
nine rows and nine columns subdivided into nine 3$\times$3
subgrids. Like the standard Sudoku, it has two basic rules:

- Each column, each row, and each box (3$\times$3 subgrid) must
have the numbers 1 to 9.
- No column, row or box can have two squares with the same
number.

Like other Sudokus published by NRICH, this puzzle can be solved
with the help of the numbers in the top parts of certain squares.
These numbers are the sums of the digits in all the squares
horizontally and vertically adjacent to the square.

#### A Short Demonstration

The square in the bottom left corner of this Sudoku contains the
number 3. 3 is the sum of the digits in the two adjacent squares,
which therefore must contain the digits 1 and 2.

In the beginning, we do not know whether we should put 1 or 2 in
the square (8,1) or in the square (9,2). If we put 1 in the square
(9,2) and 2 in the square (8,1), we have to put 3 in the square
(8,3) and 2 in the square (9,4) because of the small clue-number 6
in the square (9,3). If we put 2 in the square (9,2) and 1 in the
square (8,1), we still have to put 3 in the square (8,3) and 1 in
the square (9,4). We find that 3 will go to the square (8,3)
regardless of where we put the rest of the numbers.

At least the answer for one square is confirmed. That's not too bad
after all. Sooner or later, we shall be able to obtain the answers
for the squares (8,1), (9,2) and (9,4) as we try to solve the rest
of the puzzle.