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15. The fisr bead needs 5 lines to connect to the others; the second four (one has already been drawn); the third three, the fourth two, the fifth one; the sixth then already connects to the rest. For n beads, the general answer is: n x (n-1) / 2.

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Q: There are six equally spaced beads on a circle How many straight lines are needed to connect each bead with every other bead?
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There are four equally spaced beads on a circle How many straight lines are needed to connect each bead with every other bead?

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