Contemporary Math Problem Essay

Katherine-Claire Alston, MATH 1301 - 008, A group of 67 friends meets for lunch. They greet each other by exchanging fist bumps. How many fist bumps are exchanged if each friend must bump with each of the 66 others?

This problem asks us to determine the number of fist bumps that would occur between, 67 people, if they all fist bump each other once. This situation leaves us with two numbers to keep in mind as we try to solve this problem. The first number comes from there being 67 total people participating.The second number to remember is that each person will only fist bump 66 other people (because they will not be fist bumping themself).

There are several ways to solve this problem. One of the most efficient ways is to create a formula using the two numbers we already deemed important. Another way is to create a table that directly lays out how many fist bumps are occurring. One would create a table by consecutively listing how many students are involved in each scenario (up to the final amount, 67), and then to think about how many fist bumps would occur between each number up to 67.

While it becomes easier, once you recognize the pattern (taking the previous number of fist bumps and then adding to that number the new fist bumps the next student contributes), it is much less tedious to use a formula. However, we can use pieces of this table to check the answer we get with our formula.

The formula we will use is: We can supplement “total # of fist bumps” for “T”, total. “# of students” can be replaced by “s”, students. Using these variables we can create a shorter formula:

To find T, we need to use the numbers that we already know. “S”, the number of students is 67, making “s - 1”, 66. The new formula should look like this : Using this formula we can solve to find “T” or the total number of fist bumps. When the original number of students is 67, we will be able to determine that the total number of fist bumps is 2211.

We can double check the formula against our table. Since we have determined the number of fist bumps that comes with 5 students is 10, we should be able to get the same answer using the formula.

Since this is also correct, we can confirm that when the number of students fist bumping is 67, the total number of fist bumps is 2211. 

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