Brain Builders $\newline$ $3$ . A community center is organizing a dance. There are four large columns arranged at the corners of a square. The decorating committee will hang three large streamers from each column to every other column. How many streamers are needed?

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Q. Brain Builders

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3

. A community center is organizing a dance. There are four large columns arranged at the corners of a square. The decorating committee will hang three large streamers from each column to every other column. How many streamers are needed?

Identify Columns: Identify the number of columns and their arrangement. $\newline$ There are $4$ columns at the corners of a square. Each column will have streamers connecting to the other $3$ columns.
Calculate Total Connections: Calculate the total number of streamer connections without considering duplicates. Each of the four columns connects to three others, so $4$ columns $\times 3$ connections $= 12$ connections.
Adjust for Duplicates: Adjust for duplicate connections. $\newline$ Each connection is counted twice (once from each end), so we need to divide by $2$ to avoid duplication. $\newline$ $12$ connections $\div 2 = 6$ unique connections.
Calculate Streamers Needed: Calculate the total number of streamers needed. Each unique connection will have three streamers. So, $6$ unique connections $\times 3$ streamers $= 18$ streamers.