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

MOUSE ???? DOOR

VIE ???? SPAN

Mental Arithmetic Pays, Literally

You can barely see a newspaper these days without having their mental calculation skills questioned. Under the guise of "mental gymnastics" to "mathematical challenge" or similar, we are presented with a series of additions to perform.

Depending on the choice of the newspaper, they can be quite easy or even impossible to realize in his head. However, there are times when math pays, or at least be able to approximate the totals.

In the supermarket today I bought six items, and the project seemed too high at £ 15.49 for them. On leaving the supermarket double checked and realized that was £ very high as they were charged twice by a battery, when I had purchased a single 2.88.

So the mental calculation, or at least approximate what the total would be in my head, I saved £ 2.88. These are the prices of what we actually purchased - what would your approach of all these as they were out there?

Magazine: £ 3.25; Battery: £ 2.88, greeting card: £ 1. 49, chocolate pastry £ 3.66,: Book £ 0.89,: 0.60 pounds

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.

Sudoku variants: 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.

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?

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!

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.