93 combinatorics/alphabet.blocks.p
Description
This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.
93 combinatorics/alphabet.blocks.p
What is the minimum number of dice painted with one letter on all six sides
such that all permutations without repetitions of n letters can be formed
by placing n dice together in a line?
combinatorics/alphabet.blocks.s
n= 2 3 4 5 6
(8,4) (9,7) (9,3) (10,7) (11,7)
aijklm abcde? acdefg abcde? abkmuz
bijklm fghij? bhijkl fghij? bcpwy?
cnopqr klmno? cmnopq klmno? cdlnvz
dnopqr pqrst? dhnrvy pqrst? deqxu?
estuvw uvwxy? eiosvw uvwxy? efmowz
fstuvw afkpu? fjptwx afkpu? fgryv?
gxyz?? bglqv? gkquxy bglqv? ghnkx?
hxyz?? chmrwz lmrstu chmrwz hisuw?
dinsxz zab??? dinsxz ijoly?
ejotyz jatvx?
pqrstz
I think I can prove that there is no solution with 11 dice with 9
don't cares or with 10 dice, but I haven't checked all the details, so
I might have made a mistake. In any case, that leaves open the case
of 11 dice with 8 don't cares; my guess is that it is not possible.
-- John Rickard (jrickard@eoe.co.uk)
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