Crazy Addition is a logic puzzle produced by Conceptis Puzzles. The basis of the puzzle is the placement of digits between 1 to 9 into a square grid (normally 10x10, though other sizes are possible), following certain rules. These rules are fairly simple – digits cannot be placed in touching squares (not even diagonally), and the total number of squares used in each row and column is given, alongside the sum total of the digits.
A frequent mistake in solving Crazy Addition puzzles is to approach it with a Kakuro mindset – this will lead the unwary puzzler astray, as it is perfectly allowable for the same digit to be duplicated or even triplicated anywhere in the grid. 24-in-3 is as likely to be made up of 888 or 699 as it is to be the natural 789.
A good solving tactic is to consider the grid as a series of 2x2 squares, remembering that any 2x2 square must contain either no digits or exactly one. At the beginning of the puzzle, the aim is generally to establish as far as possible which squares contain a digit, without paying too much attention to what the digit might be. As the puzzle progresses though, it becomes profitable to narrow down exactly which digits can go where, in order to rule out further possibilities.
Fill the grid so that some of the squares (but not all) contain single-digit numbers. The blue numbers show how many digits are to be positioned in each row and column, whilst the red numbers show the sum total of all the digits. Black cells do not contain digits, and no two digits are in neighbouring squares, not even diagonally. Zero is not used in this puzzle.