At an engineering meetup, every attendee shook hands with every other attendee exactly once. If 66 handshakes were exchanged in total, how many people attended?
12 people
The formula for handshakes among n people is n(n - 1) / 2. Setting n(n - 1) / 2 = 66 gives n(n - 1) = 132. Solving the equation n^2 - n - 132 = 0 factors to (n - 12)(n + 11) = 0, giving n = 12.
About this riddle
Math riddles hide a calculation inside a short story. Pull out the numbers, work out what is being asked, and watch for a trick such as a unit change.
Difficulty: Medium. More like this: Math riddles with answers or try Target 24 for a different kind of puzzle.
More math riddles
Kai makes 2 rows of 4 chicks and adds 6 more at the end. How many chicks are there in all?
Max has 7 students. Noah has twice as many. How many students do they have together?
Leo has 19 parade floats and Ben has 4. How many more parade floats does Leo have?
Lily makes 2 rows of 2 clocks and adds 4 more at the end. How many clocks are there in all?
A bag has 20 pieces of candy. You eat 6 and give 4 away. How many are left?
Half of the 28 tulips on the table are taken away. How many tulips are left on the table?