I use this blog as a soap box to preach (ahem... to talk :-) about subjects that interest me.

Friday, November 16, 2012

Yet another book of puzzles

The last thing I would like is to put off readers of this blog by posting too many advertisements for my books. But, after all, I don’t publish things too often, do I?

I have just released a new puzzle book:

For the time being, you can only buy it from Lulu in print for AU$ 9.99 or from Smashwords in various e-book formats for US$ 1.99. It will take a while before you will find it on Amazon, Barnes & Noble, etc. It always does.

This book contains 100 difficult CalcuDoku puzzles. CalcuDokus, introduced in 004 as KenKen® (a registered trademark of Nextoy LLC), is a 9x9 numeric puzzle similar to Sudoku. But, unlike Sudoku, CalcuDoku doesn’t require you to learn complex strategies.

Each cage contains a target number and a code to indicate one of the four basic operations: “x”, “+”, “-”, and “:”. To solve a CalcuDoku puzzle, you have to solve all its cages; and to solve each cage you must write in its cells the digits that give you the cage target when you apply to them the cage operation.

Unless a cage consists of a single cell (in which case there is no operation and its solution coincides with its target), you can solve it in several ways. For example, a 2-cell cage marked “7+” admits six solutions: 61, 16, 52, 25, 43, and 34. But only one of those solutions is correct and will let you solve the whole puzzle.

You can discard the wrong solutions of all cages by repeatedly applying the rule that each digit between 1 and 9 can only appear once in each row and column.

The first sixty puzzles of this book consist of randomly generated cages, like the following one:

They are difficult, but I limited their difficulty by setting to 2 the maximum number of cages admitting more than 200 combinations. Therefore, although I haven’t tried them all, I’m pretty confident that they can be solved analytically. That is, without having to guess.

To create the other forty puzzles, I used a different strategy: instead of generating random cages, I arranged them in fixed patterns and only generated random digits, targets, and op-codes. Here is the type of puzzle you can expect:

These puzzles are in most (but not all) cases more difficult than the random ones. In fact some of them are quite diabolical. The first couple of patterned puzzles are easier than those that follow. Otherwise, the difficulty of the puzzles varies in no particular order.

Of the pattern-puzzles, I solved those numbered from 61 to 98. I haven't solved puzzle 99 but I believe it should be possible to complete it without having to guess (which I never do). Puzzle 100 is a different type of challenge: it admits two solutions, which differ in three cages. I could have removed the ambiguity by splitting one of affected cages, but I thought you might like to check it out, just for fun.

In case you are wondering, the shading of patterned CalcuDokus serves no practical purpose. It’s only there because it makes them prettier.

1 comment:

  1. This comment has been removed by a blog administrator.