# Week 2 Puzzle: Strange Dice

| 16:01 UK time, Monday, 1 August 2011

In this week’s episode of The Code, Marcus explores the mathematics of shapes and nature. In particular, he’ll be taking a look at the platonic solids, the only five regular polyhedra, and how they can be found in a number of surprising places. For most of us, its the dice Marcus uses to illustrate these beautiful, symmetrical shapes that will be most familiar.

In the show, Marcus uses a standard set of dice, each one in the shape of a platonic solids, with 4, 6, 8, 12 and 20 sides respectively.

The numbers on each face of the dice follows a very particular pattern. If you add together the numbers of each pair of opposite faces, you’ll get the same number for them all - and that number is n+1, where n equals the number of sides on that die. So the numbers on opposite faces of the six-sided die add up to seven, while those on the twenty-sided die add up to twenty-one.

This brings us to our puzzle. Below, we have the nets (the 2D patterns for creating 3D objects) of six dice. The numbers on each face, however, don’t follow the same patterns as standard dice: it’s not based on the sum of opposite faces, but on another, hidden, formula.

You have here three six-sided dice and three eight-sided dice. The three eight-sided dice follow the same pattern as the three six-sided dice. We want you to work out the pattern and figure out what number should be placed at the question mark.

Enter your answer into the Episode 2 Codebreaker using the the fourth ‘question hand’. Good Luck!

• #### Comment number 1.

Sooooo Boring.Has to be the most tediously presented programme on TV. We really did want to watch until the end but became so drowsy we had to turn over. First time ever to dismiss a programme but this was appallingly bad and 40 minutes too long.

• #### Comment number 2.

easy peasy lemon squeezy, can we make them harder next time?

• #### Comment number 3.

I didn't think this puzzle was too bad, It is a puzzle rather than just a case of eliminating obvious possibilities as the last one was and it took me a few minutes to work out exactly what was going on, even if the numbers involved generally are obvious.

The flash game is still mind-numbingly trivial though.

p.s. You probably want to resize the nets into an appropriate sized version for the blog and just link to the bigger version, most browsers are pretty terrible at scaling down diagrams and a lot of people are likely to be missing many of the lines which may well cause confusion.

Also, some indicator on the diagram of which are the opposite sides on the d8 would be helpful. As far as I can see the matching pairs are outlying 5&4, top 4 & bottom 3, top 3 & bottom 2 and top 2 & 1

• #### Comment number 4.

I too have found a solution to this puzzle - probably one of infinitely many which could map to any of the possible numbers. But the eureka feeling makes me confident.

Full marks to Marcus and team for producing the series - it's clearly impossible to appeal to the whole viewing audience but those that find it 'boring' or 'trivial', perhaps they should just go away and stop spoiling it for others.

• #### Comment number 5.

David unfortunately you have it very wrong. Found it fascinating and really well presented. Maybe it was the subject matter being too complicated for you. A brilliant series, thanks BBC.

• #### Comment number 6.

For the mosaic game, how many do you have to do to get the password?

• #### Comment number 7.

After spending a few moments looking at these nets, the solution does come pretty quickly along with that smug feeling of being right. I do have to say though that the series is amazing, much better than most of the BBC programmes nowadays that just revolve around celebrities and reality shows.

• #### Comment number 8.

Hmmm. I get the same answer doing this three different ways, but it's not one of the options on the wheel. That's annoying...

• #### Comment number 9.

Found a way to get an answer on the wheel, no idea wether its right!

• #### Comment number 10.

to wynnenc, i agree somewhat with david, but the problem isn't that the subject is too complicated but that it isn't complicated enough! there simply isn't enough maths, I have studied the platonic solids and they are amazingly wonderful shapes full of surprises, but the program didn't touch on anything more detailed than how many sides each has, and they are regular. Even just explaining why there can only be 5 would have been a start, the geometric proof is quite simple and could be easily explained with computer graphics and illustrations. Or what about considering the duel-pairs they form and how the associated spheres work together. I could mention a thousand examples.
there simply isn't enough detail, I know people often complain that the BBC dumbs things down but this just takes liberties! many other bbc programs about maths and science have been successful and still contain useful and interesting information

• #### Comment number 11.

To Livra_May.
I think that the BBC has done a great job with this series. It is like teaching maths to a class size of millions. You have to pitch the subject at the correct level to try and suit as many abilities as possible.

• #### Comment number 12.

du Sautoy uses terms such Laws, Codes and Evolution in the same sentences.

For example when I look at traffic laws I know some one had to think about those laws and put those laws into practice. A mind, intelligence was behind those simple laws, in other words a law maker.

Morse code, very simple but we all know that an intelligent mind was behind that code. What about the far more complex DNA code or the codes governing the universe am I suppose to believe that these far more complex codes came about without an intelligent code maker.

The point is: If a simple law or code needs a law or code maker then the far more complex laws and codes governing life and the universe also need an intelligent law maker.

Who or what is that law maker?
Evolution is certainly not the answer.

• #### Comment number 13.

I'm a bit confused. I haven't worked out the pattern yet (which is annoying as I'm usually pretty good at this sort of thing). But I can't see how I'd get a definite answer for "?". As far as I can see, for the 8 sided dice the only difference is in the top four numbers, as the bottom 4 are 1, 2, 3, 4 on each dice. But for the "?" there is no information to go on. If the blank sides were 2, 3, 4 the answer would be 5. If they were 2, 5, 7 the answer would be 17. You need a blank side to know the other ones. I'm probably being silly, but I can't see it.

• #### Comment number 14.

I think it's a real shame. When I first saw the description for 'The Code' on Sky, I thought it would have been a real mind-testing, almost thought provoking; a little like some of the Horizon series. The problem with such a high-brow programme on during a prime-time slot is that it has to dumb down to appeal to the masses. It seems to me that this show should really have been on BBC 4, just for its less-mass-market audience. Certainly the first show could have been divided up into two or three, which would have allowed everything to be explained in depth and really explored. It's a shame, as the BBC had a good formula for a sdhow here, it was just developed in completely the wrong way.

• #### Comment number 15.

@DannySpud: On the sheet the eight-sided dice correspond to each of the four-sided dice. I think the first two sets are examples of how they relate, and the third four-sided dice gives the key to the third eight-sided dice. But apart from that I'm as confused as you are.

• #### Comment number 16.

@boulderdash42, that makes more sense, I think. I cba to figure it out though...

The thing about this program that annoys me the most is when they keep saying "The Code" instead of "maths". It's really irritating, why are they pretending that they have uncovered some kind of da Vinci code style secret?

• #### Comment number 17.

My only disagreement with David Crabtree is with his word "drowsy". I prefer "angry". The programmes are presumably aimed at reasonably intelligent viewers with averagely enquiring minds. Why waste their time with so much repetition? Why the unnecessary camera cleverness which distracts us from the concentration which du Sautoy's core message deserves?

• #### Comment number 18.

I did notice the on the cube opposite faces all add up to prime numbers, but that doesn't seem to work for the 8 sided die. So is just a simple progression, on the cube the sides that change go 3..5..9 and 4..10..28 on the octagonal die we have 3..5..? 4..10..? and 5..17..?

If the first 2 are the same as the cube...

To my mind there should be a relationship to the physical form, and hence to something like the relationship between the numbers on opposite faces.

• #### Comment number 19.

It can be hard to see the lines on the 8 sided dice, I used a magnifier, and it became clearer to understand what was going on.
The facing sides on the 6 sided dice added up to a sequence of prime numbers for each dice, however I am having difficulty applying this to the 8 sided dice.

• #### Comment number 20.

Danny&Stuart: The blank spaces on the third d8 are actually somewhat irrelevant. Once you have the sequence you can fill them in without a problem from just knowing it's the third dice. However, more data may well help you to see a pattern, and you should be able to fill them in from observing which two numbers the top and bottom pairs always have in common.

oldunclewise: As the post says, the d8s aren't based on the sum of opposite sides. I may the mistake of adding them together initially as well. Stick with looking for a sequence in the numbers shown.

Good luck with the puzzle.

• #### Comment number 21.

Thanks IBI: yes that was a bit daft( must read instructions better!)
Another 30 mins has still not led me to it, so.....
am I looking for a sequence in the two numbers that change on each of the 6 sided dice, or a sequence of a mathematical function on two or more sides of the 6 sided dice.
Once I have this, I just apply these to the 8 sided dice.
Bizarrely, I think I can fill in the other blanks in the third 8 sided dice, just not the question mark!

53.

• #### Comment number 23.

oh no, I thought I had it, and it worked out to 53 as well (17x3)+2, but guess what? 53 isn't on the wheel!!!

• #### Comment number 24.

oldunclewise: Rather unhelpfully, it can be both. I got it as a sequence of the three(/four) numbers on the upper left(/top) half but the 1/2/3(/4) on the opposite sides could be incorporated into a formula for it. It's worth including the 2s that go with the 5,10,17 etc. in your thinking.

3n+2 isn't it, you're looking for a pattern on the dice and you'll be able to test it by filling in the blanks before you get to the question mark. Anything that only works across 5, 17 and ? is likely to be wrong.

The puzzle does involve prime numbers so it's worth having the first 15 written down in a list.

If you get an answer whose digits add up to 10 and find it isn't on the wheel then you may have forgotten to add.

I hope this hasn't been too many clues, I don't want to give out any really big clues unless they're specifically asked for.

• #### Comment number 25.

What is this "Wheel" that you talk about? Can the answer only be from some set of numbers?

• #### Comment number 26.

Another answer I got is 59.

• #### Comment number 27.

For the mosaic game, how many do you have to do to get the password?
You need to complete the game - there are 16 levels! Best of luck!

• #### Comment number 28.

Hi all,
I really enjoyd this, althouth it was very frustrating at first.
I believe that I've got the correct result as the formula works for all the dice and the result is in the options on the wheel. so if I can give a small advice:
Draw a model of 8 sided dice, cut it out, number each side, then try to form it into a dice and note down which side is opposite which. Then you can fill this up with numbers shown in the first two dice on this page. You should be able to see the formula straight away. it's obvious then and it will make sense with the 6 sided dice too. Good luck.

• #### Comment number 29.

For the Kingdom of Catapults clue I'm lost - it says the clue is on level six, but after completing the level I can't seem to find any sort of clue! Whereabouts is it supposed to be, in the opening text? After completing he level? Within the level? All that happens is I get passed on to level 7, without seeing any clue. Help! What am I missing? :(

• #### Comment number 30.

I cant believe its Friday night and I am cutting up pieces of paper to try and make dice to work this out!
I believe the opposite sides on the 8 sided dice are
1-2
2-3
3-4
4-5
and
1-2
2-5
3-10
4-17, still trying to work it out, let me know if I have got this bit wrong please!

• #### Comment number 31.

IBI, thanks for your help, i don't think you need all 15 prime numbers do you? but you couldn't give the real number you need, as that would give the game away, many thanks for not saying look at the first 50 prime numbers .
There is a lot more interesting info on prime numbers on the wikepedia page, incredible!

• #### Comment number 32.

I find these programmes fascinating and I have the greatest admiration for all you who have a go at solving the puzzles. Personnally I haven't a clue, I can't get one answer and the look of the dice just frightens the life out of me. I know I should have paid more attention in the maths lessons!

• #### Comment number 33.

I Desperately NEED some Help! PLEASE!!!!!!!

• #### Comment number 34.

Hint: Try to find a consistent formula, where the number on one side of the die can be calculated from the number on the opposite side. For instance on the first die it is simply x+1, x being the number on the bottom half of the net.

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