the deck in hopes's backyard is round. it has 5 posts evently spaced around the edge to support a trellis. for her birthday party, she wants to connect each post to all the others post with crepe-paper streamers. how many streamers will she need?

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  1. An easy way to get this answer, which will also enable you to figure it for any number of posts, is to consider each post.

    Connect the first post to each of the others. There are 4 streamers (to posts 2,3,4,5). Now, go to post #2. It still has to be connect to 3 posts (3,4,5). Then, on to post #3. It still needs streamers to 2 posts (4,5). On to post #4. It still needs 1 streamer, to post 5. By this time, post #5 has been connected to each of the other posts.

    So, adding up all the streamers, we get 4+3+2+1 = 10.

    So, you can see that for N posts, you will need (N-1)+(N-2)+...+2+1 streamers. Adding up all these numbers, you get N(N-1)/2.

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