Hi All,

This question can be solved in a couple of ways: a high-concept math approach or a "brute-force" answer that anyone can use. I'll focus on the second method.

Since we have 10 people, who will all shake hands with one another, we know that each pair of people will lead to 1 hand shake (and a person CAN'T shake hands with himself or herself).

If we call the people ABCDE FGHIJ

Person A will shake hands with BCDE FGHIJ = 9 shakes

Person B ALREADY shook hands with A, so they won't shake hands again….

Person B will shake hands with CDE FGHIJ = 8 shakes

Person C ALREADY shook hands with A and B, so they won't shake hands again….

Person C will shake hands with DE FGHIJ = 7 shakes

Notice the pattern 9, 8, 7…..the numbers will shrink by 1 with every letter, so we'll end up with…

9+8+7+6+5+4+3+2+1+0 = 45 total handshakes.

Final Answer:

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Rich

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