66 total handshakes are made. See related question at the bottom for the explanation.
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Population density.
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For a long time, people had no way to buy, sell, pay for, weigh, count, cook, measure, or build anything, and I can tell you they were getting just plain sick of it. Then one day a guy named Bernie from Cave-76 invented a system of numbers that made life much easier for everybody, and they all lived happily ever after.
28. The formula is (n * (n-1)) / 2, where n represents the number of people. You divde by 2 because each handshake covers two possibilities (ie, person #1 to person #8 is the same as person #8 to person #1).