Poor Mr. James didn't get to shake hands with everybody!

Image source: Google Images

Image source: Google Images

At a company meeting everyone showed up on time except for Mr. James. Now the presence of Mr. James was opposed by a faction of people at the meeting, and they didn't appreciate those who were tolerant of Mr. James. So before Mr. James arrived, this faction shook hands with each other just amongst themselves and then left the meeting before Mr. James arrived. Then once Mr. James did arrive, he and those people who remained each shook hands with one another. If the total number of handshakes at the meeting was 100, then how many people were in the faction that left prior to Mr. James arrival?

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Details and Assumptions:

  • One handshake is defined as two persons' shaking each other's hands using exactly one arm of each. No two-arm handshakes are allowed.
  • Nobody shakes hands with the same person (of the same faction) more than once.

Bonus: How many people were initially present for the meeting in the beginning (i.e. total people from both factions excluding Mr. James)?

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