Bunuel wrote:

The figure above shows a pattern of beads with integer diameter lengths a, b and c centimeters. This five-bead pattern is to be repeated without variation to make one complete necklace. If a : b : c = 1 : 2 : 3, which of the following could be the total length of the beads on the necklace?

(A) 56 cm

(B) 57 cm

(C) 60 cm

(D) 63 cm

(E) 64 cm

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Bunuel , or

anyone who has this crazy-making thing figured out, I am confused about "repeating."

The problem is that a necklace wraps around. See diagram:

I can make the

pattern repeat with 8 beads, if the pattern is a-b-c-b-a

I can make the pattern repeat with 10 beads, if there

must be five beads: a-b-c-b-

a-a-b-c-b-a

Must there be a repeat

a-a (and hence

five beads per "pattern")?

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"