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.
(In reply to
numerators and denominators separately by Charlie)
\ No. of dice
\
sides \ 2 3 4 5 6
2 2 2 2 2 2
- - -- -- --
4 8 16 32 64
3 5 9 17 33 65
- -- -- --- ---
9 27 81 243 729
4 10 22 46 94 190
-- -- --- ---- ----
16 64 256 1024 4096
5 17 47 125 335 917
-- --- --- ---- -----
25 125 625 3125 15625
6 26 90 290 906 2786
-- --- ---- ---- -----
36 216 1296 7776 46656
7 37 157 601 2197 7897
-- --- ---- ----- ------
49 343 2401 16807 117649
8 50 254 1142 4838 19910
-- --- ---- ----- ------
64 512 4096 32768 262144
9 65 387 2021 9819 45845
-- --- ---- ---- -----
81 729 6561 59049 531441
10 82 562 3370 18610 97882
--- ---- ----- ------ -------
100 1000 10000 100000 1000000
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Posted by Charlie
on 2021-01-27 11:06:16 |
Neatening the table
