Digital Agent Blog | OCTOBER PUZZLER
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Digital Agent engineers solve complex puzzles for our customers every day. Can you solve the Puzzle we created for you?

Josh throws a party where only cool people are invited. Everyone at the party fist bumps each other once, and there is a total of 78 fist bumps. How many people (including Josh) were at the party?

One way to solve this is by starting with small groups of people and looking for a pattern.

2 people = 1 fist bump

3 people = 3 fist bumps

4 people = 6 fist bumps

5 people = 10 fist bumps

Here we can see the pattern +2, +3, +4, and if we continue we eventually get to 13 people = 78 fist bumps.

We can also find the answer directly by labeling the party members. Use a party of 4 to start.

Person 1 will fist bump with Person 2, 3, 4 (3 bumps)

Person 2 will fist bump with Person 3, 4 (2 bumps, we’ve already counted the handshake between person 1 and 2 above)

Person 3 will fist bump with Person 4 (1 bump)

And person 4’s fist bumps have all been accounted for.

This gives us a total of 1+2+3 = 6, and we can see that this method will work for a group of any size.

We add together 1+2+3+…+12 = 78, so we know that the party must have 13 people.


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