Re: How to Make Cisterns

On 03/05/2025 13:19, David Entwistle wrote:

On Sat, 3 May 2025 11:07:57 +0100, Richard Heathfield wrote:
 

.....I cheated, and after this spoiler I offer an answer to the nearest
micron.

 In your last couple of entries, approaching an answer, the side changes by
30% and the volume changes by very little (less than 0.001%). I think
something as gone off track somewhere.

Nope. Rather than post a million results, I only posted the incremental improvements:
include <stdio.h>
int main(void)
{
   int i;
   int ms = 0;
   int mv = 0;
   for(i = 0; i < 1000000; i++)
   {
     int s = 1000000 - i;
     int v = s * s * s;
     if(v > mv)
     {
       ms = s;
       mv = v;
       printf("Side = %d microns, volume = %d cubic microns.\n", s, v);
     }
   }
   return 0;
}
[Aside to Richard Tobin - yes, I should have used long ints. Sue me.]

If you can recall high-school calculus, then the answer falls out as a
simple fraction.

I can recall passing the exam, and the answer falls out as...um... 1000000-357737 remaining=642263 removed, so the squares that were removed were each 642263/2=321131 microns on a side.
The simple fraction is therefore
  321131
-------
1000000
but that's probably not what you meant.

 

"Easily" was my immediate reaction... but then I thought about it, and
decided that it... well, that it's a far better question than it looks.

 My initial reaction was "no", but then I began to have doubts. I'll give
it a go.

Are we allowed to use offcuts to patch holes? I'm not saying I plan to try, but it strikes me that it would do no harm to ensure that the ground rules are the same for everybody.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
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