Yellow Beads
2011
how many ways can 7 diff color beads be made into a bracelet if the red blue&yellow beads must be together..?
and the purple and black beads must not be adjacent?
a bracelet can be flipped, so clockwise – anticlockwise has no meaning.
but to simplify presentation, initially let us assume that it DOES have meaning.
put RBY together anywhere and permutate.
they now form the reference ARC for the rest : 3! = 6 ways
the remaining 4 places can be now treated
as a HORSESHOE which in effect means a row
purple & black can occupy 1 -3 , 1-4 , 2-4 & permutated : 3*2! = 6 ways
the remaining colors have only 2 places; permutate them : 2! = 2 ways
so combined permutations = 6*6*2 = 72
but as clockwise – anticlockwise has no meaning, divide by 2
total # of ways = 36
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P.S.:
——
i have been asked to clarify the portion after RBY have been placed
& permutated in 3! = 6 ways
since RBY now gives a reference ARC for the rest,
the 4 remaining beads can be treated as in a HORSESHOE
(which in effect means a row)
let’s denote the 2 beads that CAN be together as T
and earmark spaces marked x for purple & black which CAN’T
x T x T x
both categories can be permutated among themselves
to give 3!*2! = 12 ways
6*12 = 72 ,
and since bracelet can be flipped, divide by 2 to get 36 ways
The Avant-Garde – Yellow Beads (1967)
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