# Super fast 3 digit dice Magic

Watch the video then see if you can tell what I’m doing.

I think this is pretty tricky and I’ve not looked into why it works yet. I’ll post the method in a while, once I’ve got to 5 comments!

Here are lists of the numbers on each dice:

Black dice:

384 483 186 285 681 780

Blue dice:

855 954 459 558 657 756

Green dice:

179 773 377 278 872 971

Purple dice:

345 741 642 147 543 840

Red dice:

564 663 960 762 168 366

(Yes, I do know they’re officially called ‘die’.)

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I have spotted that the tens value on a given die is the same so they always add up to 300. This means that one can do the following:Add the units to find tens and units values.Add the hundreds and plus 3 to find hundreds and thousands values.Is there a quicker way?

Aha!Th+H plus T+U = 50, so add units to find T+U values, then subtract that from 50 to find Th+H.Tada!

The first and last digit on each side of any die add up to the same number (7 on the first, 13 on the second and so on). The sum of those totals is 47 – with the 3 carried from the tens, that’s where the 50 comes from.Nice work, o prickly one!

Very nice, will try this out with my students! Nice to see if they can suggest other dice, extend etc….I looked at it as the sum of the first digit and the last two is constant (e.g. for 186, 1+86=87) for each die, and then if s=sum of first digits of the 5 dice, then total = 100s + 347 – s, so first two digits are s+3, last two are 47-s, and these add to 50.Funny but I didn’t notice the middle digit was the same for each number until reading the comments…. would be nice to make a set where that isn’t true, eg 879 going along with 681, 780 etcthanks, lots of fun…

Interesting stuff.As for your die/dice comment, "but both forms have been used in the singular since the 14th century":http://separatedbyacommonlanguage.blogspot.com/2006/09/die-and-dice.htmlIn addition to singinghedgehog solution, the same expressed differently can also be found here:http://www.mathpuzzle.com/dicetrick.txtI have to say, I agree with the comment made there about how you express the total. The trick would be a little better (in my opinion) if you were to express the total as a single number (e.g. eleven hundred and thirty-nine instead of one, one, three, nine). Saying it digit-by-digit suggests the individual digits on the dice are the key (which of course they are, but that’s not something you want the audience to know).

@singinghedgehog & Colin BeveridgeVery clever stuff. Well done!dborkovitzWell done also. Would be interested to hear what your students make of it.

@maxstone Good to see that about the Dice/Die thing. It’s always bugged me!That’s a reasonable point about the digit-by-digit approach. I probably will say it as you suggest in future but I will always wonder whether it makes _much_ difference to how quickly people work it out.Thanks for your comments!

@DavidGale thanks. I’m on sabbatical now, so it’ll be a while, but I do think it could be a good activity. We have a lot of blank cubes and stickers to make dice, and being able to do the trick with their friends is good motivation. Good to promote mental math too, even if it’s just a little…. and of course the patterns, reinforcement of place value etc (I teach a lot of pre service elementary teachers)

I just tried making a sets of 4 or 6 dice using similar principles…. possible to do, but it quickly made me see why whoever made up this puzzle used five dice and 300 and 47…. for example, trying 4 dice and 200 and 48, then the outer numbers need to be big and too many end up being the same …with 6 dice, the outer numbers need to be too small….. could change the 50 as total , but that’s nice….. always other bases.