Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
You are not logged in.
#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)
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)