# Calcudoku

Calcudoku is a mathematical and logic puzzle similar to Sudoku. It’s played on various grid sizes, usually from 4x4 to 9x9, though it can go even larger.

The size of the grid dictates the numbers you’ll use to fill out the puzzle. For instance, in a 4x4 Calcudoku, you'll use the numbers 1 to 4, and in a 6x6, you'll use the numbers 1 to 6.

Here’s an example of a small Calcudoku puzzle:

The objective of Calcudoku is to fill the grid with numbers so that:

• Each row and each column contains only unique numbers, without repetition (the same as Sudoku). For example, in a 4x4 Calcudoku, each row and each column should contain the numbers 1, 2, 3, and 4 with no repetitions.
• Each outlined block must satisfy the mathematical operation given by its clue. For example, if a block of two cells has the clue ‘3+’, then the numbers in those cells must add up to 3. If a block of three cells has the clue ‘6x’, the numbers in those cells, when multiplied together, should give a product of 6.

Here’s what the earlier example puzzle looks like when completed:

Because Calcudoku shares similar rules to Sudoku, we highly recommend becoming familiar with solving Sudoku before moving on to this puzzle. As you begin to solve cells in a Calcudoku grid, you can use many regular Sudoku techniques to help you solve the rest of the puzzle. Indeed, in anything beyond the most basic puzzles, you’ll need to use Sudoku techniques. You can find our complete three-part Sudoku tutorial here.

## Further Rules of Calcudoku

The Calcudoku grid is divided into several outlined blocks, and each block contains a mathematical clue in the top-left corner. This clue might be a number on it’s own (ie the contents of the cell) or it could be a number followed by an operation sign (e.g., ‘12x’ or ‘3-’), in which case the calculation must be performed on the numbers that are entered in the block.

The puzzles we publish use a variety of mathematical operators. Our kids puzzles usually only include additions, but as the difficulty level increases, so do the possible operators.

• Addition (+): The numbers in the cells of the block must sum up to the given number.
• Subtraction (-): For blocks with only two cells, one number subtracted from the other must equal the given number. Note that order matters, so if the clue is ‘3-’, and you have a 5 and a 2, then 5 - 2 = 3 is correct, but 2 - 5 is not.
• Multiplication (x): The numbers in the cells of the block must multiply to give the given number.
• Division (÷): Like subtraction, this usually appears in blocks with two cells. One number divided by the other should equal the given number. Again, order matters.

A well-designed Calcudoku puzzle (such as those we publish) has only one unique solution, and it can be reached through logical deduction. There is never any need to guess.

## Tips for Solving Calcudoku

Start with the obvious. If you see a block in a 5x5 puzzle with the clue ‘5x’ and it contains only two cells, then those cells must be filled with 5 and 1 (in some order), because that's the only way two distinct numbers between 1 to 5 can multiply to give 5.

Use a process of elimination. If you've determined certain numbers for some cells, use that information to deduce the numbers for neighbouring cells, especially within the same row or column.

Consider block position. For instance, in a 6x6 Calcudoku, a block with the clue ‘1-’ must contain a 2 and a 1 (because 2 - 1 = 1). If that block spans two rows or columns, and one of them already has a 2, then the 2 in the block must go in the other row or column.

Use Sudoku strategies. Because the two puzzles share common rules, you can use all valid Sudoku strategies to help solve Calcudoku. The more cells you fill in, the more these strategies will be helpful.

Practice. As with all logic puzzles, the more you practice, the more patterns and strategies you'll recognise, making it easier to solve more challenging puzzles.

## Where to Play

Want to try out some Calcudoku? We have you covered. We sometimes include them in our free Puzzle Weekly magazine – you should totally sign up for that if you haven’t already, as it puts 28 brand new puzzles in your inbox every week.

You can also find four levels of Calcudoku puzzles in our Jumbo Adult Puzzle Book – which happens to include more than 500 puzzles of 20 different varieties.

Puzzle Genius is an imprint of Shelfless.