A number of KenKen calculators and solvers are available online. One useful one for beginners is:
CalcuDoku, Killer Sudoku and Kakuro calculator!
If you are a beginner and uneasy about factoring and establishing all possible cage solutions, then you can use this calculator to check to see if you have found all the possibilities for solving a cage. We present the following example using the 48x cage from Problem 24 in this blog:
Above is the 48x cage. For the 5x5 puzzle we see that four numbers are required between 1 and 5. We also note that 3 doubles (or repeats of the same number) are possible: on the two sets of diagonal squares as well as in the top and bottom squares. This gives us enough information to plug into the above online calculator:
Once we have plugged in these values, we press the calculate button and generate the answer:
We see that this yields the same values that we established in the puzzle solution note:
We can look at another example, this time the 432x cage from Problem 22 in this blog:
This is a 9x9 puzzle and there is one possible double (or repeat of the same number) on the diagonal. This is enough information to enter into the calculator:
We press calculate and see the single result:
If we want to figure this out logically, without the calculator we start by breaking down 432 to its prime factors:
2 x 2 x 2 x 2 x 3 x 3 x 3
We can see right away that 1 cannot be used, since 1x9x9 (the maximum number solution) is nowhere near 432! We must now multiply some of these numbers together so that we are left with three numbers from the set 1 through 9.
If we start at the low end and convert 2x2 into 4, we are left with 2x2x3x3x3 and there is no way to make two numbers under 10 from these factors. If we start with 2x2x2=8 then we are left with 2x3x3x3 and we can see only one way to combine these into two numbers we can use: 2x3=6 and 3x3=9. So we get the single possibility: 6x8x9.
We can work through a similar argument starting from 3 at the high end of these factors and arrive at the same conclusion: 6x8x9.
FACTORING HELP
For those who merely want help factoring a large number, there are a number of straight factoring calculators available. Remember, however that 1 is always a factor and is often used. One good calculator is:
from Calculator.Net
If you plug in 432 from the above example you get the following result that breaks down the factors in several different ways. For KenKen solvers, the PRIME FACTORS are the important ones since they give you the base to work out what possibilities can be used for any particular cage:
