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

You are not logged in.

## #1 2006-10-21 19:53:18

George,Y
Super Member

Offline

### 6 Frogs Want The Other Side

6 Frogs are on a trunk across a small, say, river, 3 facing 3. They wanna get to the other side and none of them would back up to show timidness. A frog can leap forward one step or two steps so long as there is a room for it to land. Now a space for only a frog lies in between of the two groups  and they sit close to each other. Like this
///_\\\
The question, how can they swop the position with the other side and get this?
\\\_///

Apparently after the first step the positions could be
either //_/\\\ or /_//\\\
for convenience, let us use o instead of _ to express the empty space.

It may take you some tries though.

X'(y-Xβ)=0

## #2 2006-10-21 21:34:04

mathsyperson
Moderator

Offline

### Re: 6 Frogs Want The Other Side

Well, that second option you gave is a dead end straight away, so we're left with //o/\\\.

Now we can move another left frog into the space, but that would get us back to the dead end that we already rejected, so we're left with //\/o\\.

And then it starts to get a little tricky, because we now have more than one option that has options coming off it. The main thing you need to watch out for is to make sure you don't make any //\\ groups.

Why did the vector cross the road?
It wanted to be normal.

## #3 2006-10-25 13:45:59

George,Y
Super Member

Offline

### Re: 6 Frogs Want The Other Side

Indeed, some sheer trial'n'error

X'(y-Xβ)=0

## #4 2006-10-31 06:35:22

Jena
Novice

Offline

### Re: 6 Frogs Want The Other Side

I got a slightly different solution and it appears to take one shorter step, unless I'm going crosseyed. How do I do the little "solution" button to post mine (and get someone to check it!)?

Edit: Nevermind, I realized I misread a detail in the original problem. Bother!

Last edited by Jena (2006-10-31 06:40:48)