Given d dice each with n sides, find the probability that when they are rolled at once, there are no two consecutive numbers.
This task may be quite difficult. For a warm-up, try finding the numerators for fixed d such as {1,2,3} or for fixed n such as {2,3,4}.
Note 1: I don't have a formula so much as an algorithm.
Note 2: This problem arose as an attempt to solve http://perplexus.info/show.php?pid=12342 by Larry which uses non-independent cards instead of dice.
number of dice
sides 2 3 4 5 6
2 1/2 1/4 1/8 1/16 1/32
3 5/9 1/3 17/81 11/81 65/729
4 5/8 11/32 23/128 47/512 95/2048
5 17/25 47/125 1/5 67/625 917/15625
6 13/18 5/12 145/648 151/1296 1393/23328
7 37/49 157/343 601/2401 2197/16807 7897/117649
8 25/32 127/256 571/2048 2419/16384 9955/131072
9 65/81 43/81 2021/6561 1091/6561 45845/531441
10 41/50 281/500 337/1000 1861/10000 48941/500000
>>
|
|
Posted by Charlie
on 2021-01-28 16:18:58 |
reduced fractions
