Brian's Place

Puzzles & Brain Teasers

Sudoku

The name Sudoku comes from syllables selected from a Japanese phrase, the whole phrase being loosely translated as: "The numbers must occur only once".

In the above solution (adding the red numbers) to the original puzzle (the black numbers), every row, evey column and every 3 by 3 square contains all of the digits 1 to 9, each occurring only once.

The squares need not contain numbers. It's the same game if you replace each digit with any other token, such as a kind of fruit or the picture of a well-known movie star.

For more information, see the following links.

Information About Sudoku

Everything you could possibly want to know about Sudoku

In other words, the very comprehensive article on Sudoku in Wikipedia.

It tells you more than you probably want to know about the game, including many strategies for solving it.

Sudoku links

This is a large, active set of links about Sudoku, from the Open Directory Project.

Many strategies for solving Sudoku

Here you will find a big list of solution strategies, including a few that are intended for automatic solving by computer, and are therefore completely pointless if you like solving puzzles yourself!

The Sudoku Solver

This is a major piece of work by Andrew Stuart.

Don't get put off by the advanced stuff (even some of the so-called simple stuff is pretty advanced) - it's best to start solving Sudoku using simple approaches.

However one of the fascinations of Sudoku lies in the discovery of its unexpected subtleties, which this site will really help with.

Play Sudoku

OK, so you know about the strategies for solving Sudoku, and you want to find some puzzles to solve!

Here are a few suggestions:

Web Sudoku

The most popular Sudoku site on the Internet, created by Gideon Greenspan and Rachel Lee.

You can generate any number of Sudoku games, selecting your level of difficulty.

Once you have a game on the screen, you can print it and play it offline, and/or you can complete it online (with electronic pencil marks allowing several tentative entries per cell, if you want) and check each move as you go along.

Important:

Select the Options button before the first time that you start to play!

JigSawDoku

A Flash-based presentation of essentially the same game, also produced by Rachel Lee and Gideon Greenspan.

This is more fun than the first one in some ways (e.g. you can substitute symbols for numbers, and see and move all the unused numbers or symbols). However it doesn't have pencil marking or the same flexibility on the hint system.

Other Web Browser Based Sudoku

This is a subset of links about Sudoku, from the Open Directory Project.

Free Online Puzzle Games

If you are looking for free online Sudoku puzzles, see above.

However, there are lots more! For example...

BLOXORZ

This game is simple in concept (like many of the best games) but is great fun and totally addictive.

A 2-by-1 block is moved across a tiled floor by rolling it sideways or lengthwise ninety degrees at a time.

The aim is to get the block to fall into the square hole at the end of each stage.

There are 33 stages to complete. You can return directly to any stage that you have already reached.

Bridges and switches are located in many levels. The switches are activated when they are first pressed down by the block.

Soft switches (round-shaped) are activated by any part of your block.

Hard switches (X-shaped) need the block to be standing on end in order to get enough pressure to activate them.

Some switches open or close bridges alternately. Some switches will only ever make certain bridges open, but won't close them.

Orange tiles are fragile. A block standing vertically on one may make the tile give way.

Teleporting switches, shaped like ( ), teleport your block to different locations, splitting it into two smaller blocks. These can be controlled individually and will rejoin into a normal block when both are placed next to each other.

Small blocks can't activate heavy switches, and can't pass through an exit hole without being rejoined into a complete block.

That's it! You can play the game here...

Lots More Free Online Puzzles

If you are looking for free online Sudoku puzzles, see above.

For a pictorial index to lots of other free online puzzles, go here.

It you prefer normal text descriptions, go here.

You will also find lots more free games of all kinds at FreeWorldGroup.com.

Have fun!

Brain Teasers

This section contains two great problems in logical thinking.

You don't need to be sitting in front of a keyboard in order to wrestle with these!

The first one is a pure logic problem, which totally killed all productivity in the place where I was working for a couple of days. We got there in the end... but it's a toughie.

The second one is a great example of how counter-intuitive the notion of probability can be.

The Lying Blackfoot, The Truthful Whitefoot... and the Random Greyfoot

If I remember correctly, this first appeared as a prize puzzle in the English Sunday Times, around 1970.

It is a diabolical variation on a simpler puzzle, which we need to look at first:

The Simpler Version

A jungle island is inhabited by two tribes, the Truthful Whitefeet (who always tell the truth) and the Lying Blackfeet (who, as you suspect, always lie). Unfortunately apart from their feet they look pretty much the same, and since they always wear moccasins, you can't tell them apart.

Also, they get distinctly annoyed if you ask too many questions, which is not a good thing in these parts.

Also, they only answer Yes or No to anything you ask them, and they will ignore you (and get annoyed) if you ask a question for which Yes or No wouldn't be a sensible answer, or indeed address any other kind of remark to them.

An explorer arrives at a fork in the path, at which is standing such a tribesperson. The explorer is desperate to find the village which he knows is nearby. If he takes the wrong fork, he will probably perish from one of the numerous perils that lurk in this jungle, including dying of thirst.

He knows that he had better ask just one question (to be on the safe side) in such a way that whether the answer is Yes or No, he will know which fork in the path will take him to the village.

He could, of course, point to one of the two paths, and ask: "Is that the way to the village?" But he could have the bad luck to be talking to a Lying Blackfoot, and this is no time to be depending on luck.

He knows that he had better not ask the tribesperson to take off his (or possibly her) moccasins either, in order to get a readout on the colour of the feet, since this will severely annoy him (or possibly her)... which is known not to be a good thing to do.

After much cogitation, he comes up with a question. The tribesperson grumpily answers "No". "Thank you," says the explorer, and with much relief takes off down the correct path to the village.

What was the question that he asked?

If you know the answer, carry on! If you don't, try to work it out... and if you can't (please try first!) you will find the answer here.

The Diabolically Hard Version

A very similar jungle island is inhabited by three tribes, the Truthful Whitefeet (who always tell the truth), the Lying Blackfeet (who always lie) and the Random Greyfeet who simply answer Yes or No at complete random (they must toss a mental coin, or something... anyway they have no malicious or benign intent when they say Yes or No, it really is random, OK?). Unfortunately apart from their feet they look pretty much the same, and since they always wear moccasins, you can't tell them apart.

These tribespeople have very similar characteristics to those on the other island, except for two differences:

1. They are just a little bit less easily annoyed than the tribespeople on the other island (but don't push your luck!).
2. They always move around in a threesome, one person from each tribe (maybe because it isn't safe to let a Random Greyfoot wander around on his (or possibly her) own).

Our intrepid explorer once again encounters a fork in a path, and he is in the same mess as he was before. Standing next to the fork is a threesome of tribespeople (the explorer knows that this must consist of a Blackfoot, a Whitefoot and a Greyfoot, since they always travel around together).

His safest option is to ask just one question to one of the three tribespeople, but unfortunately the question he used before won't work, because he could have the bad luck to pick the Random Greyfoot, and whatever his question was, the answer wouldn't tell him reliably what he needed to know.

Sweating profusely, he realises that he is going to have to push his luck a bit, and ask two questions. He could ask the same tribesperson two questions, or maybe put one question to one of the tribespeople and the second question to another of the tribespeople. Anything more, and they will all get severely annoyed... which would not be a good thing.

He starts to panic... and then (because he has an extremely logical brain, however foolish he might be in choosing to wander around these jungle islands) the solution comes to him.

He chooses one of the tribespeople (going "eeny... meeny... miny... mo..." under his breath) and asks his first question. "Yes," grumpily answers the tribesperson. He then asks his second question, and the tribesperson that he asks glowers threateningly and wonders if this scrawny object could possibly be good to eat, but finally answers "No". "Thank you," says the explorer, and with much relief takes off down the correct path to the village.

What were the two questions that he asked? And how did he pick which tribesperson to ask the second question to, if that matters?

If you work out the answer, or you have tried hard to work it out but need some help, I would be only too pleased to hear from you - please e-mail me!

Let me reassure you, though: there is an answer, and it is not based on gimmicks, just pure logic like the simpler version is. Also, whatever the explorer's solution is, it doesn't depend on luck (other than testing the temper of the tribespeople) - if he gets answers at all, then he is guaranteed to get the information he needs.

Answer To The Simpler Version

The key to this version of the puzzle is that the explorer has to get the same answer, irrespective of which tribe the person comes from. Finding the key of the puzzle is really important (as it will be with the harder version)!

The explorer points to one of the two paths at the fork (the incorrect one, as it turns out), and asks: "If I were to ask you if that was the way to the village, would you say Yes?"

A Truthful Whitefoot (let's assume he's male) knows he would say No if asked, and has to tell the truth about this, so he answers No, meaning that he would not say Yes if asked.

A Lying Blackfoot (let's assume he's male) knows he would say Yes if asked the same question (he would lie), but has to lie about this fact, so he answers untruthfully No, meaning that he would say No if asked (which is a lie). Both tribespeople would be forced to answer the same question with the same answer, because the Lying Blackfoot is tricked into lying about how he would lie, and so ends up giving the same answer as the Truthful Whitefoot - which is what is wanted in this desperate situation!

If that makes sense to you, you're ready for the harder version!

The Monty Hall Problem

This problem is associated with the American television game show artist, Monty Hall - hence its name.

You will find a good description of the problem, and the controversy it created, here.

Even when you have discovered the correct answer, you may still not believe it. A good explanation can be found here in Wikipedia.