Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

Login

Username

Password

Not registered yet?

#1 2005-09-18 01:13:56

asebon
Guest

the houses and the fountains

There are three houses in a row and in the other side there are three fountains each house must take water from each fountain without the pipes intersecting. The problem must be solved in two dimensions

#2 2005-09-18 01:18:35

kylekatarn
Power Member

Offline

Re: the houses and the fountains

It can be proven that such problems (connecting each one of 3 houses to 3 resources)  are impossible.

There is no solution on a 2D plane.

#3 2005-09-18 01:28:06

kylekatarn
Power Member

Offline

Re: the houses and the fountains

let's connect 2 houses (H1 H2) to all resources (each one of the three fountains - F1 F2 F3)
http://adsl.xl.pt/kylekatarn/3houses.JPG
It doesn't matter the position of the three fountains. When you "fully connect" 2 houses, you block one fountain.

I think this type of problems can be studied with Graph Theory - networks.

Last edited by kylekatarn (2005-09-18 01:30:15)

Board footer

Powered by FluxBB