Friday, January 03, 2014

The Christmas Investigations - Crystal Maze

Christmas Investigations
Part Three
In the third of our Christmas Investigations we take a look at one of of the most popular game shows in the UK. Based on the French game show Fort Boyard; The Crystal Maze is a show everyone remembers fondly, the question is:

How do you decide when it is in your teams favour to buy someone out?

My very own Crystal
In the show a team of contestants would try to complete challenges in return for crystals. These crystals would earn the team time in a final game where they could win some fabulous, or not so fabulous prizes.

The team were guided through four different 'time zones' by their host, first Richard O'Brien and later Edward Tudor-Pole. The four original zones were set in an Aztec clearing surrounded by temples; an Industrial warehouse, a Medieval castle and a Futuristic space-station, later a sunken Ocean liner joined the ranks of zones.

The challenges were fiendish tests of mental agility, skill and physical capabilities as well as the devious 'mystery' games which covered more or less everything. In todays investigation we give you the chance to tackle some of the series' puzzles before setting you the ultimate Crystal Maze dilemma.

The Greek Cross

A whole series of geometric puzzles involve moving a series of pieces which form a cross so that they instead form a square - or indeed vice-versa. These Greek Cross puzzles rely on the related geometry of the two shapes, and the pieces, in order to work.

One such puzzle was featured in the Crystal Maze in the Medieval zone. You'll need a piece of cardboard, a pencil, some scissors a ruler and a set-square or something with a known right-angle.

This is the diagram you need to draw out. Each square on the grid represents about two centimetres. That means that your cross will have sides of four centimetres long, and will be twelve centimetres across. You can of course scale this up but I wouldn't make it much smaller, as any error in the measuring has a greater effect.

The first line to cut across your cross goes from the lower external corner of the left hand arm of the cross diagonally to the opposite internal corner.

The second line passes through that internal corner at right angles to the first line. It should run from the centre of the top edge to the middle of the bottom edge of the right hand arm of the cross. Apart from the gridlines your diagram should look like the one to the left.

Once the diagram is drawn cut it out, and cut along the two dissection lines leaving you with four pieces as in the picture to the right. All you need to do now is arrange the pieces into a square. In two and a half minutes, with a presenter chuckling in the background.


The fantastic characters of Mumsie and Aunty Sabrina, both played by Sandra Caron; also resided in the Medieval zone ready to challenge contestants to a game of riddles. The player would have three minutes to answer any one of three questions correctly. They only got to give one answer for each question.

The questions were usually mathematical conundrums, rather than riddles. Many of them are what the Wandering Puzzler would call spoken operation sequence understanding or reversal puzzles, others included a bit of hidden information and some algebra. On The Desert Forges however they call them Jidis - a much neater name.

Here then is your chance to take on three of Mumsie's finest.

Mumsie's Riddles

1. In our armoury is a line of eleven spears lined up from the shortest to the longest. The difference between each one and it’s neighbour is 10cm, the longest one is three times the length of the shortest, how long is the longest spear?

2. I was late for the theatre yesterday and missed a quarter of the play, if I have been a quarter of an hour earlier I would have missed only one eighth.

How long was the play?

3. A maiden was given a box of sweets. She ate half of them on the first evening and each evening afterward she ate half the number of sweets left from the day before. On the sixth evening when she went to the box she found there was only one left.

How many were in the box originally?

Three Cubes

A third and final puzzle from the Medieval zone  now, and one that will take a little more of your craft skills. What you need are three cubes, they all need to be approximately the same size.You could use building blocks or dice and paint them with acrylic paints as I have done below. Alternatively you can print out a cube net and use this to construct your cubes.

Once you have your three cubes you need to decide on three different designs to put on the faces. If you want to be authentic you could use the original designs, my artistic ability is somewhat limited so I went for plain, coloured faces. 

You need to follow these guides exactly when applying the designs to your cubes, otherwise the puzzle could be insolvable. I recommend numbering your designs on a handy piece of paper, so you don't lose track of which is which. 

Once your cubes are finished, all you need to do is stack them in such a way that there are no identical symbols on any one side of the three-cube high structure you have made. There is just one key thing to realise about the geometry of the cubes, once you have it, the puzzle is child's play.

The Prisoners Dilemma

We're not looking at the usual prisoner's dilemma here, note the apostrophe, but the even more challenging dilemma of whether to release captive teammates in The Crystal Maze. 

Each challenge in the game had an element of risk and reward; complete the game and you win a crystal, but fail to escape in time and you get locked in. It is possible to buy back a lost teammate with a single crystal.

In the end game each of these crystals is worth five seconds of time inside the Crystal Dome. Inside all the remaining teammates spend the time trying to collect gold credits while avoiding silver ones. The credits are blown around by a huge fan, and the flashing lights make separating the colours difficult.

All the silver credits collected are subtracted from the total gold credits collected, if the team score more than 100 credits after deductions  they win some spectacular prizes, not just for themselves but also for any teammates who were left locked in. 

As you can see there is a fine balance between having more hands collecting credits at the end, and having more time to collect with. Many team captains struggled with the decision of how many teammates they should buy out when they had only limited crystals. In fact, a very simple bit of mathematics can give you the answer. 

The Christmas Investigation

Louise is the team captain of a team being led around The Crystal Maze by Richard O'Brien. Things were going quite well at first but in the last five games the team have suffered five lock-ins. Louise is the only person left and there is just time for her to buy out any teammates she wants to take to the Crystal Dome to help collect credits. 

She does a quick bit of maths and realises that the best thing she can do is buy out all of her teammates since buying out four, or five has the same effect and if she buys out all five everyone gets the experience of being in the Crystal Dome. 

Given all of the above information, how many games did the team win before their disastrous run of lock ins?

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