Bumping question

[kavitha]

The residents of Nogginbumpin greet each other by bumping heads. At a gathering, a total of 55 bumps were exchanged. If each person bumped heads exactly once with every person there, how many residents attended?

 

[tkhunny]

You need a strategy. Simplify often works.

If two came: One Bump
If three came: Three bumps
If four came: Six Bumps

It may also be useful to ponder a parity issue. Each bump takes two heads. Maybe not.

Would it be easier if you lines them up and had the first person in line bump heads with everyone else. For example: Five people, names A, B, C, D, and E.

Line them up:

ABCDE

Have A bump everyone

AB, AC, AD, AE and then run off to the other room.

Have B bump everyone.

BC, CD, BE and then run to the other room

Have C bump everyone.

CD, CE and then run to the other room.

Have D bump everyone

DE and run to the other room.

We started with five and produced a pattern 4, 3, 2, 1 - making 10
If we start with 4, we might get 3, 2, 1 and that's six! This is consistent with the original claim.
If we start with 3, we might get 2, 1 and that's 3.

I think we're done.

 

[Denis]

Google "handshake puzzles"

 

[Buttercup]

Bump

Interesting...