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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?

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?

Full solution

Q. 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?
  1. Identify Columns: Identify the number of columns and their arrangement.\newlineThere are 44 columns at the corners of a square. Each column will have streamers connecting to the other 33 columns.
  2. Calculate Total Connections: Calculate the total number of streamer connections without considering duplicates. Each of the four columns connects to three others, so 44 columns ×3\times 3 connections =12= 12 connections.
  3. Adjust for Duplicates: Adjust for duplicate connections.\newlineEach connection is counted twice (once from each end), so we need to divide by 22 to avoid duplication.\newline1212 connections ÷2=6\div 2 = 6 unique connections.
  4. Calculate Streamers Needed: Calculate the total number of streamers needed. Each unique connection will have three streamers. So, 66 unique connections ×3\times 3 streamers =18= 18 streamers.

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