The DeciMate encryption scheme requires a sequence of true random decimal digits.
The sequence will be hand-generated by throwing a set of dice to determine each digit.
The dice are perfect cubes with 6 blank faces.
Any number or symbol can be written on each face.
Design such a set of dice so that each sum 0 through 9 has exactly the same probability.
** 6 cannot be used as a 9 by turning it upside down.
one way (same as Jer's solution)
1st die has: 0,1,2,3,4, "reroll this die"
2nd die has: 0,0,0,5,5,5
1.2 rolls (of the first die) is the expected number of rolls to get a definitive number 0 to 9.
another way
1st die has: 12,9,6,3,0,-3
2nd die has: -2,-1,0,1,2,3
Sum the 2 dice. 16 of 36 times, the sum will be less than 0 or more than 9.
But each sum 0 through 9 will come up 2/36 times.
Thus, outcomes 0 through 9 are equally likely.
If you don't get 0 to 9, reroll both dice.
1.8 rolls is the expected number of rolls to get a definitive number 0 to 9.
The specific numbers on the dice for this second way are not unique; there are probably many solutions of this type.
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Posted by Larry
on 2023-12-03 19:00:59 |
Another type of solution
