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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1. 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?

2. 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!

3. 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!

4. 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…

5. 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).

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

7. 8. 9. 