Summer Kakuro

INTRODUCTION What is Kakuro? Kakuro is an extremely addictive puzzle game -- a test of skill and logic. Allyou have to do is place numbers 1 to 9 on the puzzle grid. Easy! Or is it? Only one arrangement of numbers will give the correct answer. It canbe seductively simple or it can be mind-bending. This book contains 201 Kakuropuzzles at four levels of difficulty (Piece of Cake, Tea Break, Lunch Break andAll Nighter) -- enough to satisfy beginners and addicts alike for hours on end. How to play Kakuro The diagram overleaf shows a small Kakuro puzzle. The objective is to placenumbers 1 to 9 in the white cells on the grid, so that each row or column ofadjoining white cells adds up to the total printed in the dark grey cell totheir left (for a row) or above (for a column). The light grey cells do not playany part in the game. YOU MUST place the numbers 1 to 9 in the white cells in the unique arrangementso that all the column and row totals are correct. YOU MUST NOT repeat a number in any continuous row or column of white cells. How to crack Kakuro Begin by looking at the totals (the dark grey cells) -- these are your firstclues. For example: Looking at the puzzle shown, and starting in its simplest area, the bottom row,there are two white cells that must add together to make 3 (the value marked inthe dark grey cell to their left). We know that 1 + 2 = 3. Any other combination of two numbers between 1 and 9,where no number is repeated, will add up to a value greater than 3, so this rowmust contain 1 and 2. All we have to do now is determine the order in which they should appear: is it[1,2] or [2,1]? To do this we must look at the neighbouring cells. Look first at the two cells in the row above. We are told these contain twonumbers that add to make 4. 1 + 3 is the only combination of two numbers thatadd to make 4, without repeating a number (2 + 2 would repeat the value 2). Look next at the far right column of the grid. It contains two numbers that addto make 3, so we know it must contain a 1 and a 2 (using the same reasoning thatwe used for the bottom row). So which number goes in which cell? Let's try a few combinations and see how we get on. First we will try placingthe numbers 1 and 2 in the bottom row in the order [2,1]. If we do this we must place a 2 in the last cell of the row above, to make thefar right column add up to 3. However, as this cell's row must be made up of a 1and a 3, to give a total of 4, placing a 2 must be wrong. Therefore we must go back and try placing the numbers in the bottom row in adifferent order [1,2], and then follow the same logical steps to see if thisresults in a better outcome. As we can see, all the numbers we have placed now add up to the correct columnand row totals without repeating any value in any row or column. In fact, theyalso allow us to make the leap quickly to filling in a 2 in the only open whitecell in the fourth column, to give the required column total of 6. In larger puzzles, several continuous blocks of white cells may appear in asingle row (as in a crossword). While you must not repeat a value in anyadjoining white cells, you may repeat values across the whole row or columnproviding they fall in separate groups of white cells. The example below shouldexplain this clearly: As can be seen, the numbers 1 and 3 appear twice in the top row. This isperfectly correct as they do not appear more than once in either of the twoontinuous blocks of adjoining white cells. Conclusion When you first see a Kakuro puzzle, you may think it is all about maths. Don'tbe fooled. And don't panic. It isn't. Only simple sums are ever used and theseare repeated time and agaiSinden, Pete is the author of 'Summer Kakuro ', published 2007 under ISBN 9780743297509 and ISBN 0743297504.