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Suguru is a captivating number puzzle. At first glance it looks like a broken Sudoku grid. But whilst it shares some commonalities with its more well-known cousin, Suguru is a different kettle of fish altogether. If you’re new to Suguru, have a look at our tutorial here to get started.
One of the techniques that’s fundamental to solving harder Suguru puzzles is elimination by implication. We are going to look at some examples.
To start us off, we’re using a puzzle taken from A Year of Suguru (Easy to Intermediate) - the puzzle is from June 14 if you have the book and want to play along, and complete the rest of the puzzle yourself.
Here’s the grid as presented in the book:
Let’s begin with an interesting example near the middle of the puzzle. I’ve highlighted two regions, green and red. The red region has no clue numbers in it at all, but we can still use it to solve the green cell with the ? inside:
We can solve this cell purely through implication. We know that the red region must contain the numbers 1, 2 and 3 (because it contains three cells). It doesn’t matter what order they appear in that region, they will all affect the highlighted green cell because they are all adjacent to it either vertically or diagonally. That means our green cell (the one with the ?) cannot contain a 1, a 2, or a 3. It also cannot contain a 4 because that already appears in the green region. Therefore the only number that can go there is a 5.
Even though the neighbouring region contained no clue numbers, its size and position made it useful. This was an example of simple implication. The implied contents of one region allowed us to directly solve a cell in a neighbouring one. But implication can go further.
Let’s turn our attention to the bottom right of the grid. I’ve highlighted four regions that have some interesting interplay.
We’ll begin with the green region. Given the presence of the 2 in the blue region above it, we know that the top cell of the green region cannot contain a number 2. Therefore the number 2 must go in one of the two bottom cells. This is a simple implication.
Because we now know that one of those two cells has to contain a 2, we can further imply that the left-most cell in the yellow region cannot be a 2. It doesn't matter which of the green cells is a 2, they both prevent the left-hand yellow cell from containing a 2. As there are only two cells in the yellow region, the left-hand cell must be a 1, which leaves the right-hand cell as a 2.
We’re not done yet. We can also infer, using the green region and the yellow one, combined with the blue one, that there’s only one place to put a 2 in the red region:
Here’s where it gets fun: the 2 we just filled in inside the red region now has a knock-on effect on the green region, telling us which of our two candidate cells must contain a 2 – the bottom one, it’s the only possibility.
Just by inferring that one of the bottom green cells must contain a 2, we’ve been able to fill in a neighbouring 2, which then allowed us to figure out another neighbouring 2, which in turn let us come back full circle and figure out which of the green cells must contain the 2! This is an implication chain at work, albeit a small one. They can get much, much longer.
Here’s another example of an implication chain. This is the May 25 puzzle from the same book as above, if you want to play along. Here’s the empty grid, and I’ve highlighted three green cells that we can fill in through implication initiated from the red region. Can you work out how?
We’ll start with the 3 in the red region. This is a handy corner cell which eliminates three neighbours in the region just to the right. We can imply the position of the 3 in that region, narrowing it down to two possible cells, like this:
Even though we don’t know which cell contains the 3, we do know that either way, we can eliminate two cells in the region below. Furthermore, the 3 in the neighbouring yellow region knocks out two more cells, leaving only one place to put our 3:
That 3 then gives us the position of the 3 in the region to the right:
That in turn tells us where the 3 goes in the next region up:
Phew - after all that, even though we didn’t yet work out the position of the 3 in the first region, we could still use its implied position to fill in three other cells in the chain.
Implication chains are a powerful tool for solving more difficult Suguru puzzles. Even if a simple implication doesn’t let you fill in a cell, it’s worth trying to follow the chain because you never know where it will lead. It may even lead back in a circle, letting you fill in the original cell.
Chains can often come in handy for getting you moving if you get stuck, but they are just one tool in the toolkit for Suguru-solvers. Don’t get hung up only looking at chains, when often simple elimination will get you to a result more quickly.
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We are huge fans of ereading devices here at Puzzle Genius. iPads, Kindles, Kobos, we use and love them all. It’s one of the reasons our free weekly puzzle magazine is designed to work on devices (as well at having a printable section).
Last month, Kobo introduced a brand new colour ereading device – the Kobo Libra Colour. We knew as soon as we saw it that this was going to change everything. Not just because it’s the first colour ereader from a major ebook retailer, but because like some of their larger devices, it offers stylus support.
Stylus, you say? That means it’s perfect for puzzle solving!
Kobo readers have by far the best annotation system we’ve seen. The ability to write directly on the page is almost made for puzzle books. So of course, we had to bring our books to the Kobo store.
We could have just re-released some of our old titles and been done with it, but that would be to do a disservice to Kobo owners and to our readers. Instead, we have launched a brand new series dedicated to Kobo readers. New puzzles, designed specifically for Kobo.
Our new series – Puzzles For Stylus Devices – has been designed from the ground up to take advantage of Kobo’s best-in-class annotation features. All the books in the series are designed to use the full width of the screen to give you the biggest puzzles possible. That means when, for example, you’re working your way through a Sudoku, there’s plenty of room for notes and candidates, even on the 7” Libra Colour.
We’ve also made full use of interactivity, so that you can simply tap an icon to switch between a puzzle and its solution.
We’re launching Puzzles For Stylus Devices with the following books:
Each book in the series features one hundred puzzles – all brand new, never published before in any of our other books.
Using an ereading device like a Kobo has some pretty big advantages for puzzlers. For one thing, you can fit the whole series of books into a device that’s small enough to fit into a bag or jacket pocket. Our Pocket series is undoubtedly convenient, but even we have to admit you’re probably not going to carry around ten different puzzle books in one go. On a Libra, or even the slightly bigger Sage, you can bring a whole library with you wherever you go, weighing just a couple of hundred grams.
There’s also the handy ability to be able to erase errors without leaving a trace. Naturally you, dear reader, are an expert puzzler and never make mistakes. But for those mere mortals among us, being able to erase a wrong number or shape and have another go without leaving any evidence of our misdemeanour is an attractive proposition!
The Puzzles For Stylus Devices series is designed for all Kobo stylus-compatible readers. Right now that means:
The Elipsa comes with a stylus in the box. The smaller Sage and Libra are sold without a stylus, to keep their prices as affordable as they are. You don’t have to buy Kobo’s stylus (excellent though it is) – any Microsoft Surface-compatible stylus will work. That includes the Metapen M1 and M2, and the Renaisser Raphael 520C. And of course Microsoft’s own Surface Pens will work too. These alternatives come in at under half the price of Kobo’s stylus.
To celebrate this brand new series, we have launched with an introductory price of just £1.99 / €1.99 / $1.99 per title – huge value! See the full range of books here. And don’t forget to check back regularly as we have plenty more titles on the way. Happy on-screen puzzling!
Ancient logic puzzles have been a cornerstone of intellectual development and entertainment throughout history. These puzzles, originating from various civilizations, not only provided amusement but also played a significant role in the development of critical thinking and problem-solving skills. This post delves into the origins, cultural impact, and evolution of these ancient conundrums, drawing connections to their modern-day descendants.
The Birth of Logic Puzzles in Ancient Civilizations
The earliest forms of logic puzzles can be traced back to ancient civilizations like Egypt, Greece, and China. These puzzles were often integrated into myths, religious practices, and the daily lives of the people. For instance, the famous Greek myth of the Labyrinth and the Minotaur is an early example of a maze, a type of logic puzzle that involves finding a path through a complex network.
In China, the I Ching, also known as the Book of Changes, used a system of hexagrams to predict the future. This can be seen as an early form of a logic puzzle, requiring deep understanding and interpretation of abstract patterns.
Cultural Impact and Significance
These ancient puzzles were not merely for entertainment. They held significant cultural, educational, and philosophical importance. In Egypt, for example, hieroglyphs, which were a combination of logographic and alphabetic elements, presented a form of puzzle to decipher the language. This deciphering process honed skills in pattern recognition and logical thinking.
In Greece, philosophers like Plato and Aristotle used logical puzzles in their teachings to develop critical thinking skills. These puzzles were instrumental in the evolution of deductive reasoning and the scientific method.
Evolution of Ancient Puzzles into Modern Forms
Over the centuries, these ancient logic puzzles have evolved into various forms that we recognize today. The transformation can be seen in the evolution of mazes and labyrinths into more complex puzzle designs. Modern puzzles like Sudoku, which originated in Japan, owe their lineage to these ancient forms of brain teasers.
Linking to Modern Puzzles
Today's logic puzzles, such as Sudoku, are deeply rooted in these ancient traditions. They continue to challenge our minds and provide entertainment, much like their ancient counterparts. For those interested in experiencing a modern twist on these ancient challenges, exploring Puzzle Genius's diverse range of puzzles, including a mixed variety, can be a delightful journey through history and logic.
Continuing the Legacy: Ancient Logic Puzzles in Today's World
In today's digital age, ancient logic puzzles have found new life. Websites like this one offer a plethora of puzzles, including comprehensive guides like Sudoku From Scratch, which provide insights into solving modern puzzles that have their roots in ancient logic games. Additionally, for enthusiasts seeking regular updates and new challenges, subscribing to Puzzle Weekly offers a weekly dose of (free) brain-teasing fun.
The journey of ancient logic puzzles from their earliest forms to the present day highlights the enduring appeal and intellectual stimulation these games provide. They are not only a testament to human creativity and intelligence but also a bridge connecting past and present, traditional and modern, in the world of puzzles.