Puzzle Madness
Not logged in. [Register (free)][Login]

Mathdoku Techniques

This is our starting grid for our example. What people usually find most intimidating about Mathdoku puzzles the first time they tackle them is that there is no obvious starting point.
Best place to start is to look for a group of cells that have limited possibilites. Look at the two hilighted cells, these have a constraint of 4*. There are two ways of satisfying this constraint, either with the sum 2*2=4, or, 1*4=4.
But, by having 2*2 we would have to place the number 2 in that column twice, which breaks the rules of Mathdoku. Our solution must be 1*4=4, we don't know yet which order they go in, but we can write some pencil marks in.
Similarly, we can look at these two hilighted cells as well. The only valid combination here is 2*5.
Again, we don't know which way round they appear, but by adding some pencil marks we are adding more constraints to our puzzle and eventually a number will present itself.
Solving Mathdoku puzzles require using an advanced Sudoku technique known as naked pairs. We've just put the numbers 2 and 5 in our hilighted cell. We don't know which way round these numbers appear, but we know for certain that they must appear in those two cells. This removes them as possibilites for the rest of the row.
By eliminating 2 and 5 from the remainder of the row, this only leaves one possibility for our hilighted cell, and that is 6/3=2.
Look at our hilighted cell in this instance. By using the naked pairs technique we can eliminate the numbers 2, 3, 5, and 6 from our hilighted cell.
We know already that the cell to the left must contain a 1 or a 4, we don't have enough information here to make narrow it down any further, so our hilighted cell must be 1 or 4.
We now have enough information to fill in the hilighted cell!
For that section the constraint is '2/'. We already know that the other cell must be a 1 or a 4. So let's look at the possibilites.
Our only possibilites are 2/1=2, or 4/2=2. We don't have any other possibilites, so whichever sum is the correct one, our hilighted cell must be 2!
By continuing on this way, we can insert another two sets of pencil marks as shown here.
But, we can use the naked pair technique here again. Look at row 5, the two left-most cells have a 3, 6 naked pair, whcih means we can eliminate 3 and 6 from the remainder of that row.
This only leaves one remaining possibility for our hilighted cell, it can only be a 5! This also means we can fill in the cell above it, this must be a 3.
The key to a Mathdoku puzzle is finding the starting point, once you have a starting point you are continuously adding more and more constraints and making the puzzle easier!
Want to complete this puzzle? Play online now!