By Henry Kwok
interactive version of this puzzle.
Rules of Bochap
Previously, I have created puzzles which used only one of the
four mathematical operations ($+$, $-$, $\times$, and $\div$). In
this Sudoku I have combined all the four operations together in a
single puzzle. I call my new puzzle 'Bochap', which comes from a
popular Hokkien word in Singapore.'Bochap' can be interpreted as
'oblivious to everything else'. Thus, the name of this new puzzle
suggests that puzzlers are so focused on finding a solution that
they reach a point of being 'Bochap' or oblivious of everything
going on around them.
This reminds me of the story of Archimedes who, as he was
drawing some diagrams on the ground, was approached by an invading
Roman soldier who drew a sword over his head and asked him who he
was. Too much absorbed in the diagrams on the ground, Archimedes
did not give his name but, protecting the dust with his hands,
exclaimed: "Don't disturb my circles!" As a result, he was
slaughtered by the Roman invader!
Like the standard Sudoku, this puzzle has the basic
- Each column, each row and each box (3x3 subgrid) must have the
numbers 1 through 9.
The puzzle can be solved with the help of small clue-numbers
which are either placed on the border lines between selected pairs
of neighbouring squares of the grid or placed after slash marks on
the intersections of border lines between two diagonally adjacent
Each small clue-number is the result produced in any order by
a pair of digits in the two squares that are horizontally or
vertically or diagonally adjacent to each other, using the
mathematical operation indicated: addition ($+$), subtraction
($-$), multiplication ($\times$), and division ($\div$).
The position of each pair of diagonally adjacent squares is
indicated by either two forward slash marks // or two backward
slash marks \\.
The clue \\14+ on the intersection of border lines between the
diagonally adjacent squares (r6c2) and (r7c3) means that possible
pairs of numbers in the squares are: 7 and 7; 6 and 8, 8 and 6; 5
and 9, or 9 and 5. The clue 3$\div$ on the border line between the
squares (r9c4) and (r9c5) means that possible pairs of numbers for
these squares can be from the following combinations: 1 and 3, 3
and 1; 2 and 6, 6 and 2; 3 and 9, or 9 and 3.
After finding the values of all the unknown digits, the puzzle
is solved by the usual sudoku technique and strategy.
A word document containing the Sudoku problem for classroom
use, can be found here