Re: 11 year olds homework

From: Phil Carmody (thefatphil_demunged_at_yahoo.co.uk)
Date: 11/14/04 

Date: 14 Nov 2004 14:06:27 +0200

Angus Rodgers <angus_prune@bigfoot.com> writes:

> On 13 Nov 2004 12:31:19 -0800, chrissmith_156@yahoo.co.uk
> (Chris) wrote:
>
> >My 11 year old cousin got this question for homework.
>
> I never got homework this hard when I was 11 (or when I
> was 18, for that matter)!
>
> >I cannot find a solution.
>
> I think I'm on the way to a solution, but it's past my
> bedtime, so I'll reluctantly have to stop.
>
> >Am I missing something very obvious
>
> I don't *think* so ...
>
> >or is there simply no solution?
> >
> >http://geocities.com/chrissmith_156/question.gif
> >
> >By "repeat this process until you stop" I assume it means
> >until each corner turns to zero,
>
> It's badly worded, but I also assume that's what it means.
>
> >which usually only takes 3-7 recursions. Unless
> >you start using very big numbers...
>
> I couldn't face experimenting with lots of numerical examples ...
>
> >Any ideas?
>
> ... so I tried working backwards, i.e. looking at all configurations
> requiring 0 steps, then 1 step, then 2 steps, and so on.
>
> This got a little too complicated --- quite quickly --- so I deviated
> from the logic a bit. Here are the cases I've looked at so far:
>
> [A] All four numbers are zero. Then 0 steps are required.
>
> Assume from now on that not all four numbers are zero. Then some
> positive number of steps is required.
>
> [B] All four numbers are equal (but nonzero). Then one step
> (exactly) is required.
>
> Assume from now on that not all four numbers are equal. Then more
> then one step is required.
>
> (Easy so far!) :)
>
> [C] Any two numbers diagonally opposite one another are equal (but
> not all four are equal). Then 2 steps (exactly) are required.

For values of 2 occasionally near 4:

bash-2.05b$ ./square.pl 1 3 1 5
Stage 1: 1 3 1 5
Stage 2: 2 2 4 4
Stage 3: 0 2 0 2
Stage 4: 2 2 2 2

Phil 

-- 
They no longer do my traditional winks tournament lunch - liver and bacon. 
It's just what you need during a winks tournament lunchtime to replace lost 
... liver.   -- Anthony Horton, 2004/08/27 at the Cambridge 'Long Vac.'

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