## PUZZLE |

**Calcudoku Puzzle Rules**

The rules of Calcudoku Puzzles are as follows:

- Place the numbers 1-6 once in each row and column of the grid. There is no 'box' constraint in calcudoku.
- Bold-lined regions contain a number and mathematical operation (addition, subtraction, multiplication, division). The digits within the region must match the given sum.
- With subtraction sums, you must subtract the smaller numbers from the largest number in the bold-lined region. With division sums, you must divide the largest number by the smaller numbers in the region.
- Numbers are allowed to repeat within bold-lined sum regions, as long as doing so doesn't break the rule that a number cannot repeat within a row or column.

Here is an image of the start position of a Calcudoku puzzle:

There is a lot to digest in the rules above. First, it is worth pointing out that it is unusual in a sudoku variant for repetition to be allowed, and it is important to bear this in mind. That's particularly true if you are used to playing killer sudoku puzzles, which calcudoku builds upon by also introducing subtraction, division and multiplication, since in killer sudoku numbers cannot repeat within sum regions.

Look at the 36x yellow region in the bottom-middle of the image above. Due to repetition being allowed, and the shape of the region, the values could be 6,1,6. However, if the 36x region was in a straight vertical line, then that wouldn't be possible, as then having 6,1,6 would mean the repetition of a number in a column, which is against the rules. It can take a little bit of getting used to.

The other thing to point out that can confuse is the way that the subtraction and division regions work, as outlined above. The addition and multiplication is easy: that's because 2+3 is the same as 3+2, and 2x3 is the same as 3x2. However, that's clearly not the case with subtraction and division: 2-3 is not the same as 3-2 and 3/2 is not the same as 2/3 (note that the puzzles use / to indicate division).

In other words, with subtraction and division, order matters. Therefore it's key to bear in mind that you must find the highest number in each division and subtraction region, and subtract from that number, or divide it by the other numbers, as relevant. Thus, the 4- in the bottom right of the example grid above must contain 6 and 2 or 5 and 1 in some order. But it doesn't matter whether the actual order is 2,6 or 6,2 or 5,1 or 1,5 since the rule is, as explained, however they are actually arranged, you perform the calculation in the specified order.

If you would like a visual explanation of the rules of calcudoku, here is a video that explains the rules:

**Play A Sample Calcudoku Puzzle**

If you'd like to have a go at solving the Calcudoku puzzle shown above now that you know the rules of the game, you can play via our Online Calcudoku Puzzle Player

Once you have solved the puzzle if you tried it (or got stuck and want to see how to solve it), then you might also find the video below interesting, that walks through how to solve the puzzle:

If you enjoy this puzzle type, you can join our online Puzzle Connoisseur's Club for £12 or $17 a year and play a new Calcudoku Puzzle puzzle every day of the year, together with many other fun and interesting logic puzzles.

**Strategy and Solving Tips for Calcudoku Puzzles**

The video above walks through the solve of the sample puzzle, and in so doing reveals some of the logic that can be used to solve calcudoku puzzles. It's important to note that all our calcudoku puzzles can be solved using logic alone, and no guessing is ever required to reach the single solution. Here are a few strategy tips:

- Identify the sum regions with just one option first: for instance the 10x region in the example puzzle (middle-left) must be 2 and 5 in some order. This means that the rest of the row must contain 1,2,3,4 in some order. The 6/ region in row two must contain 1,6 in some order.
- You will almost certainly need to use pencilmarks to keep track of what can go where in all but the easiest calcudoku puzzles. The online player makes it easy to do this (press the spacebar if you have a keyboard to toggle between big numbers and pencilmarks).
- It is often worth looking at sum regions and working out which numbers can't be placed in them. For instance, the 36x region cannot contain a 5, since 5 is not a factor of 36. Looking at row five, the 5+ sum clearly cannot contain a five, nor can the 6+ sum made from three squares contain a five, which means there is only one place the five can possibly be placed in row five: the final square in the row.