Puzzle Blog

Hashi Puzzles

Hashi is a puzzle that requires you to connect a series of islands with a set of bridges.

It is a fun and relatively simple (in most cases) Japanese puzzle that also goes by the name of bridges, funnily enough.

Each island contains a number and you simply need to connect the islands to each other with the stated number of bridges on each island, but no more than two bridges may connect any two islands to each other, and bridges must be horizontal or vertical and cannot cross. Finally, no island can be isolated: it must be possible to walk from any island to any other island using the bridges alone.

To play a sample bridges puzzle and get printable Hashi PDF puzzles you can play Bridges Puzzles at the Puzzle Club.

Fillomino Puzzles

Fillomino is a rarely seen Japanese puzzle variant.  The grid contains a range of numbers that indicate groups of cells that must be adjacent to each other.  For instance a ‘3′ means there are 3 cells that form a group together, such that you can move from one cell to any other by moving just horizotally or vertically from one member to another. 

Groups of the same number cannot touch either horizontally or vertically (otherwise they would not be groups of that number if you think about it), but the most interesting rule is that you often have to add new groups and work out the number(s) in these.  For instance you might have to quite often add groups of size 1 - 4, but on occasion you need to go larger and sometimes surprisingly high numbers are forced uniquely through the constraint that groups containing the same number cannot touch.

To play some fillomino puzzles online, try the hand-made puzzles here:

http://www.thepuzzleclub.com/fillomino.php

There are other fillomino online but so far I have only seen computer generated fillomino.  Unfortunately the examples I have seen are not really true fillomino in the sense that they tend to contain a high number of 1’s in the grid, and this appears to be to constrain the rule that you sometimes have to add regions yourself - I have never seen one of the generated puzzles that requires you to add regions which defeats most of the fun of the game and what makes fillomino so unique and different to other puzzles.  If anyone knows of other fillomino puzzles that require the use of this fascinating rule please post them in the comments.

What is hanjie and how do you play it?

Hanjie puzzles have been around for a long time, but they are still unknown to many puzzle players.

You may have played hanjie under a range of names - it has been known variously as tsunami, hanjie, nonogram, griddler and probably more besides.

The aim is to work out which cells in each row and column of the grid-based puzzle must be filled in.  To help decide this, at the edge of each row and column are a series of numbers that tell you how many cells are filled in that region.

For instance, it could say ‘5,2′ - this means there are five filled cells and another region of two filled cels that are consecutive.  A comma denotes a gap of at least one cell between filled regions (otherwise it would be 7 if there was no gap!), but the gap can be many more than one cell.

The puzzle is solved through cross-referencing, and making gradual progress each time through with the harder puzzles.

Some things are easy to work out - for instance if all or none of the cells in a row are to be filled then you can fill them in straight off.  If more than half of the cells are to be filled, then you can fill the middle cell(s).

For instance, if the row is five cells in length and you know that 3 cells are filled, then in any combination the middle cell must be filled in, therefore you can fill it in.

Likewise, you can also make progress by working out cells that are not filled too, as this can further constrain options for the various regions and columns.  To mark a cell that cannot be filled may hanjie players like to put a dot in the cell.

At the end of the puzzle you will reveal a simple black and white image, and a clue to this is often given at the start of the puzzle.  Depending on how good the puzzle artwork is, the image may be more or less easy to recognise at the end!

You can play hanjie online by clicking that link, and also at the online Puzzle Club.

Lateral Thinking Puzzle

Once upon a time, not so very long ago, there was a street swindler named Shady.

Shady used to offer everyone that walked past the chance to win a priceless diamond, but only if they could guess which hand it was in.  In the other hand, was a coin, choose the coin, and lose, he used to say.  And everyone did lose.  To add to the drama, Shady would open the chosen hand palm down over a ‘try again’ container which the unlucky loser would, each time, see the worthless coin, and their hopes of fortune, drop into.

His stand on the street was very tempting, as it was surrounded by treasure chests full of precious stones, or at least precious looking, which tempted in the eager and occasionally greedy punter who thought they could take on Shady.  Only they always lost, and went away empty handed, greasing Shady’s hand with a pound coin every time.  No-one took the hint from his name that Shady was less than honest, and in fact, everytime he used a little magical flair to switch the diamond for another coin, so in fact he always had two coins in his hand.

Today Our Hero walked up to the stand (call him Fred), and did what no-one else had done - won!  How did he win without having to show in any way that Shady was using underhand tactics to win?

Sudoku variants: smileydoku

smileydoku

Here is a puzzle to cheer up the first day back after the bank holiday here in the UK… a smileydoku!

The rules are as per standard sudoku, except that there are three additional regions. These are marked in grey and contain nine cells, and each must contain the numbers from 1 - 9 exactly once only. So the smile is not just symbolic here - it demarcates three additional regions of the puzzle.

See how long it takes you, hopefully once finished you will still be smiling rather than frowning! It is not too difficult, but you will need to use the additional regions to help you solve the puzzle.

To view the puzzle as a PDF either click the image above, or this link to smileydoku.

Maths Challenge Puzzle

Maths related puzzles can provide a simple and focussed challenge - performing mental arithmetic as quickly as you can without making mistakes can actually be quite good fun!

Here are three maths challenge puzzles for you, an easy, a moderate and a hard puzzle. See if you can do them within a minute. The level of these is very fair with only a gentle increase in difficulty at each stage, so none of the calculations expected are unreasonable such as calculating 37.5% of a number or squaring 34! If you want harder ones, let me know.

The Missing Link

Here is a fun word puzzle with various names, such as link word, chain word and so on.

All you need to do is find the one word that joins the word on the left and the word on the right to create new words or phrases in each case.

For instance, if you have something like this:

HAND ???? THING

… then the answer could be SOME to make HANDSOME and SOMETHING.

Here are three:

SHIP ??? STICK

VIE ???? SPAN

From A to Book Fair

Today I went to the London Book Fair. As usual it was pretty busy, and most people were moving from meeting to meeting or wandering around. Or queuing for food or drink.

Trying to move about efficiently with so many people getting in your way is pretty hard.

For todays puzzle, if you wanted to travel to five different stalls just once, how many possible combinations are there? And how does this increase with the more stalls you have to visit. Can you work out the formula for the number of possible routes you can take if you have to visit n stalls?

Going Bananas…

It is a not so well-known fact that the best day of the week to pick bananas is a Monday. Allegedly. How many reasons can you come up with as to why this might actually be true?

This is a lateral thinking puzzle, so no idea is necessarily too outlandish - feel free to post any reasons you come up with! But don’t drive yourself bananas thinking about it…

Mental Arithmetic Pays, Literally

You can barely see a newspaper these days without having your mental arithmetic skills challenged.  Under the guise of a ‘mental gym’ a ‘maths challenge’ or similar, we are presented with a series of sums to perform.

Depending on your choice of newspaper, these can be fairly easy or almost impossible to really do in your head.  However, there are occasions where maths pays, or at least being able to approximate totals.

At the supermarket today I bought six things, and the bill seemed too high at £15.49 for them.  On leaving the supermarket I double checked and realised it was £2.88 too high as they had charged twice for a battery, when I had only bought one.

So mental arithmetic, or at least approximating what the total would be in my head, saved me £2.88.  Here are the prices of what I actually bought - what would your approximation of the total of these be as you were going around?

Magazine: £3.25; Battery: £2.88, Greeting card: £1.49, Chocolates: £3.66, Pastry: £0.89, Paper: £0.60