Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2005-09-17 03:13:56

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 2005-09-17 03:18:35

kylekatarn
Member
Registered: 2005-07-24
Posts: 445

### 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.

Offline

## #3 2005-09-17 03:28:06

kylekatarn
Member
Registered: 2005-07-24
Posts: 445

### 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 (2005-09-17 03:30:15)

Offline