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'Ratio Sudoku 3' printed from http://nrich.maths.org/
By Henry Kwok
Rules of Ratio Sudoku
Like the standard sudoku, this sudoku variant has two basic rules:
- Each column, each row and each box (3x3 subgrid) must have the
numbers 1 to 9.
- No column, row or box can have two squares with the same
The puzzle can be solved with the help of small clue-numbers
which are either placed on the border lines between selected pairs
of adjacent squares of the grid or placed after slash marks on the
intersections of border lines between two diagonally adjacent
The small clue-numbers are ratios or fractions of two digits
in the two squares that are horizontally or vertically or
diagonally adjacent to each other.
Each fraction is written in its lowest terms, with the smaller
number denoted as the numerator. Thus 1/2 can stand for the
following combinations of numbers in the two adjacent cells: 1 and
2, 2 and 1,2 and 4, 4 and 2, 3 and 6, 6 and 3, 4 and 8 or 8 and
Suppose the answers in the two adjacent cells of a puzzle are
actually 7 and 5, the clue-number will be written in the form 5/7
instead of 7/5, otherwise this would give away the answer and the
puzzle would be too easy to solve!
The position of each pair of diagonally adjacent squares is
indicated by either two forward slash marks // or two backward
slash marks \\. For example, the //(4/5) on intersection of border
lines between the diagonally adjacent squares (8, 6) and (9, 5)
means that possible pairs of numbers in the squares are 4 and 5 or
5 and 4. The \\(1/7) on intersection of border lines between the
diagonally adjacent squares (6, 2) and (7, 3) means that possible
pairs of numbers in the squares are 1 and 7 or 7 and 1.
The bracket symbol ( ) is used to separate the slash marks //
or \\ from the fractions on the border lines between the diagonally
adjacent squares. For example, it is obvious that //(3/5) is
preferable to //3/5.
Finally, the clue-number 2/3 on the border line betweeen the
squares (3, 6) and (4, 6) means that possible pairs of numbers for
these squares can be from the following combinations: 2 and 3 or 3
and 2, 4 and 6 or 6 and 4, 6 and 9 or 9 and 6.