Do You Play Number Games?

Variations of Sudoku

There are many variations of Sudoku. Some of the variants have additional constraints that complicate solutions significantly. I use to play two of them, Killer Sudoku and KenKen.

• Killer Sudoku 

This variant adds a new dimension to classic Sudoku. The grid consists of areas (cages) that are outlined with grey or dotted lines. There are no starting clues! Instead, a total of each area is given. Numbers inside an area, when added together, should make a number shown in the upper left corner of that area. All the rules of the normal Sudoku apply - each number appears exactly once in every row, column, box and cage. It is really brain teasing because more than one combination of numbers gives the required total value. 

Below is one of the world's hardest Killer Sudoku. You can try to solve it here. 

• KenKen

KenKen is a sophisticated arithmetic and logic puzzle invented by a Japanese mathematics teacher in 2004. He developed a brain-stimulating exercise with the main goal to improve student's math and logic skills. KenKen is similar to Killer Sudoku but with additional constraints - operations. The target numbers in the top corner of each heavily outlined area (cages) are produced by using the mathematical operation indicated behind the numbers (+, -, ×, ÷). 

I find KenKen more challenging than classic Sudoku. It is a great exercise for practising mental arithmetic. The difficulty level increases depending on the size of a grid. The hardest KenKen puzzles are Black Belt KenKen. 

Worldwide Sudoku Championship

World Sudoku Championships are held annually since 2006. The very first competition was held in Lucca, Italy, in 2006. The most successful winner is from Japan, having won the title four times. Also, Japan is the most successful team. 

World's Hardest Sudoku Puzzles 

Arto Inkala is a Finnish mathematician (doctor of science in the field of applied mathematics). He is also a passionate puzzle creator who created some of the world's most difficult and challenging Sudoku puzzles:  ‘AI Escargot’ in 2006, and ‘the thing Everest’ in 2012.

The Miracle Killer Sudoku is an extremely hard puzzle created by Philip Newman. It seems unsolvable because only 18 cells are covered by cages. Sudoku fans proclaimed the puzzle one of the most incredible ‘sudokus’ of all time. If you want to try to solve it, here is a link to the puzzle. If you need hints for solving, here is a link to the video on the most popular YouTube's sudoku channel, in which the solution is explained in detail.

But the hardest puzzles are created by computer programming. There were much larger puzzles with 16 × 16 or even 25 × 25 grids and a three-dimensional version in the form of a cube.

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There are many more interesting facts about Sudoku and its variants. Sudoku is fun and fascinating and the most popular logic game in the world. The fact that many mathematicians are fascinating by Sudoku explains a lot about this puzzle and the sophisticated mathematics behind it. 

Is it addictive? Yes! But as with many things in our life, moderation should be practised. 

I leave you with a paraphrase of the well-known saying:

One or two Sudoku a day keeps the doctor away. 

And what about you? Do you play number games? 

Title Image: Sudoku GIF, Source: Wikimedia Commons