KenKen is an arithmetical logic puzzle developed by Japanese teacher Tetsuya Miyamoto as a brain-training device in 20041. It is a popular variant of a Sudoku puzzle in that the user will be trying to fill out a square grid of length i with the digits [1 thru i] (inclusively) appearing only once in each row and column. While Sudoku exclusively employs 3x3 squares (for standard 9x9 puzzle) as it's tertiary constraint, KenKen instead defines free-form "cages", the "cells" of which serve as arguments to an arithmetical operator to evaluate to the "target" value for that cell.

The jargon is more intimidating than the puzzles themselves. Let's begin by defining our terms.

Terms
Cell - a single entry square in the puzzle grid
Column - a vertical series of i cells in an i x i square grid
Row - a horizontal series of i cells in an i x i square grid
Cage - a thick-bordered region constraining the arithmetic operation
Target - the number to which each cage ought to evaluate
Operator - the arithmetic function to be employed betwixt EACH of the values the user enters to every cell of a given cage
Objective
The objective of any i x i square grid of KenKen is to evaluate all arithmetic operations such that the numbers [1 - i] appear once (and only once) in each row and each column of the puzzle
Rules
The digits 1 thru i appear once and only once in each column
The digits 1 thru i appear once and only once in each row
The digits of each cell within a given cage will evaluate to the target of that cage when the given operator is applied between each cell value
Strategies
Identify "Freebies" - a cage which is 1 cell large has only one solution: the target value (the implied operator is =)
Identify 'Large Boundary Conditions' - a cage comprised of two cells, with a + or × operator which can only reach target with cell values (i) and (i-1)
Identify 'Small Boundary Conditions' - a cage comprised of two cells, with a - or ÷ operator which can only reach target with cell values (i) and (1)
Continue to evaluate rows and columns for clues (solved cages) which will reduce the evaluation of complex cages
Operators
- - subtraction (5-3=2)
* or × - multiplication (5×3=15
/ or ÷ - division (6÷3=2)
^ or ** - exponent (5**3=125)
% - modulus (5%3=2... 5÷3 is 1.667. {5 - (1*3)} = 2)
// - integer division (5//3=1)
= - equals

Example KenKen puzzle2

```
___ ___ ___
|5+ |   |3+ |
|___|___|___|
|4+ |3+ |   |
|___|___|___|
|   |   |3  |
|___|___|___|

```

Solution method
1 - start at the lower right corner - this is a Freebie. The value can only be 3.
2 - Since there is one 3 in the bottom row, no other cells in that row can be 3. The cage to the lower left must evaluate to 4 - we cannot have two 2's in the same column, so this cage must contain both a 1 and a 3. Knowing that the bottom row has a 3 indicates that, for this cage, the 3 must be above the 1.
3 - The center cell of the bottom row must be 2 to solve that row. The second cell in that cage must be 1.
4 - The top left corner cage now has three clues for two cells. We know they must add to 5, we know there is only one available value to solve the left column, we know there is only one available value to solve the center column. The top left corner cell must be 2, and likewise the top middle cell must be 3.
5 - The top right corner cage now has three clues for two cells. We know they must add to 3, we know there is only one available value to solve the top row, we know there is only one available value to solve the center row. The top right corner cell must be 1, and likewise the right middle cell must be 2.

Solution to Example KenKen puzzle2

```
___ ___ ___
|  2|  3|  1|
|___|___|___|
|  3|  1|  2|
|___|___|___|
|  1|  2|  3|
|___|___|___|

```

Sources
1 - Wikipedia. "KenKen". Accessed 11/28/2018.
2 - KenKenPuzzle.com. "How to solve". Accessed 11/28/2018.

IronNoder 2018: 15/30

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