Simon’s True Gems

Just look at those precious mathematical jewels!


And just think of all the tricks you can come up with!



Simon’s favourite trick, something he learned from Matt Parker, is quickly calculating the sum of all the faces he can’t see (the faces of the dice that stack on top of one another):


The thing is that two opposite faces on every die always sum up to the number of faces plus one (21 in the case below, as an icosahedron has 20 faces):


And 13 on the next picture, because a dodecahedron has 12 faces. To say the sum of the faces you can’t see you simply calculate n (number of faces) + 1 and multiply that by the number of dice, minus the top face.



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