Oulun Lyseo / Galois-club
Mathemagic 6
1. Guessing the dice total
HOW TO DO IT?
a) Give a spectator three dice and ask her to throw them on the table while you are not
watching (you might be in another room during the next step b)
b) Ask the spectator (i) to add the three face numbers [say 2+4+5 = 11], (ii) to pick up
one of the three dice [say the one showing 4 and add its bottom number to the previous
sum [11+3 = 14] and (iii) roll this dye again and add its new face number [say 6] to the
previous sum [i.e. 14+6] to get the final sum [20] and write it down on a piece of paper
hidden from you. (You will be able to guess this final sum.)
c) After the spectator has completed the above process she invites you to look at the table
where the three dice are lying as they were left after the throws as described in b).
What you see are the face numbers 2, 5 and 6. Even though you do not know which one
was rolled again you can calculate the final sum to be the visible face sum 2+5+6 = 13
plus 7 which makes 20, the right answer.
WHY IT WORKS?
The trick is based on the 7-principle or the fact that the pairs of opposite faces of a normal dye
are (1,6), (2,5) and (3,4) and so the opposite faces always add up to 7. When the spectator
picks up the dye with face number 4 and adds its opposite face number 3, then the total sum
will be equal to 2+5+7. When the same dye is rolled again to give 6, the final sum will be
2+5+6+7 can be calculated just by adding 7 to the three faces that you see when you return to
the table.
2. Guessing the sum five faces
HOW TO DO IT?
a) You turn your back and instruct the spectator to form a stack of three dice, one on top
of the other. Then ask him to [i] add the two faces which are touching on the top and
middle dice (say 1 and 4) and [ii] add to this sum (5) the touching faces of the middle
and bottom dice (say 3 and 5) and [iii] finally add to this sum (13) the bottom face of
the bottom dye (say 2).[You will be able to this final sum (15) of five faces.]
b) Ask the spectator to keep the final sum hidden from you and only tell you the number
on the top face of the top dye (6). Then you can announce the total sum of five faces by
simply subtracting the top value from 21 to get 21 – 6 = 15.
WHY IT WORKS?
This trick is also based on the 7-principle. The sum of all six horizontal faces in the stack must
be 3x7=21. Subtracting the top face leaves the required sum of five faces.