Step 7 Dec 2010 Puzzle

L D[AR2P#0.0] · Dec 23, 2010

Four rabbits start at the four corners of a 32x32m field. A farmer fires his gun and each rabbit starts running in an anti-clockwise direction and chases after the rabbit in the next corner. Eventually the rabbits end up in a flurry in the middle of the field.

Using PLCSIM, write a program that shows the trajectory of the rabbits from the starting gun using the Q outputs arranged as below. The rabbits are shown in their starting positions.

Supplementary question - How for does each rabbit travel before they meet in the middle of the field?

Seasons greetings to all.

504bloke · Dec 23, 2010

The farmer wasnt a very good shot then was he

Merry Christmas

Thomas_v2 · Dec 23, 2010

Hi,
should the rabbits be able to do diagonal steps, or only one step in x or y direction like the tower in chess?

L D[AR2P#0.0] · Dec 23, 2010

Any steps you like.

Peter Nachtwey · Dec 23, 2010

It is an iterative process. The and x,y rabbit position should be kept track of using REALS.
After each update the real value can be truncated or round to integers for ploting. The result should be a 'swirl' converging on the center.

daba · Dec 23, 2010

Which rabbit did the farmer shoot?

Where I come from, he wouldn't have missed, so he's a dead 'un, and the one to his clockwise (rabbit_2) wouldn't have anything to chase, so he'd sit there doing sweet f.a. He realises there's no point running after a dead rabbit! He can be considered lazy, or clever.

That means his "chaser", rabbit_3, would run straight at him, along the side of the square, to the next CCW corner.

Rabbit no.4 therefore chases him to the same corner, and will take a diagonal run to meet him where he intercepts with lazy/clever rabbit.

I can't see how they meet in the middle to enjoy their MacDonalds Ice-Cream.

But it don't matter, because the farmer has had ample time to reload, and with suitable Buck-Shot, can take the other 3 rabbits out with one more shot after they have converged at said corner.

Put a big pot on the stove - rabbit stew for tea I think !!

Tharon · Dec 24, 2010

daba said:
Rabbit no.4 therefore chases him to the same corner, and will take a diagonal run to meet him where he intercepts with lazy/clever rabbit.

Even if rabbit 1 is dead, rabbit 4 wouldn't run in a straight line towards rabbit 2, he'd start off running straight towards rabbit 3, but rabbit 3's position is changing, so rabbit 4's path is kind of "curving" towards the stationary rabbit 2.

I wish I had enough time to play with the math to find their paths... I'm sure there is a way to make an equation to find their positions.

Thomas_v2 · Dec 24, 2010

The farmer is a clever one.
First he shots in the air and the rabbits are running around until they meet around the middle - where he does all of them with one single shot...

I think he has to wait 30 steps before they meet in the middle.
"Bresenham line algorithm" is a good starting point for programming this.

L D[AR2P#0.0] · Dec 25, 2010

Here's my flurry:-

Thomas_v2 · Dec 25, 2010

My path is looking slightly different:

L D[AR2P#0.0] · Dec 25, 2010

You have a flaw in your algorithm or your plotting logic.

Here's a simple example solution I found using bugs instead of rabbits:

TurpoUrpo · Dec 26, 2010

Nice one

Here is my first try to it. Its not identical to ld's solution, but pretty close.

L D[AR2P#0.0] · Dec 26, 2010

Looks good to me. How about the question of how far does each rabbit travel ?

TurpoUrpo · Dec 26, 2010

Here is iteration two with more accuracy + travel.

Thomas_v2 · Dec 26, 2010

I'm already curious about your "rabbit logic".
My rabbits are pretty dumb. On each iteration they check which axis (x or y) to the next rabbit is the nearer one, and do one step in the resulting direction, or a diagonal step when near enough.
It's fast, but it's not drawing nice lines...

Step 7 Dec 2010 Puzzle

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