Does anyone have any intuitive proof for this 1400?

Revision en2, by Luckwet, 2025-08-28 21:25:16

C. DIY (ICPC2024-2025)

Let's say we can choose 4 points to make a rectangle. Let the numbers defining the coordinates be arranged in ascending order: a, b, c, d.

Then I have a question. Is there any INTUITIVE proof that it is advantageous to take exactly

xmin = a

ymin = b

xmax = c

ymax = d ?

And not, for example, as I thought at the very beginning

xmin = a

ymin = b

xmax = d

ymax = c.

I have already done the MATHEMATICAL proof, but now I need the INTUITIVE proof.

History

 
 
 
 
Revisions
 
 
  Rev. Lang. By When Δ Comment
en3 English Luckwet 2025-08-28 22:39:44 0 (published)
en2 English Luckwet 2025-08-28 21:25:16 2 Tiny change: 'eginning\nxmin = a' -> 'eginning\n\nxmin = a' (saved to drafts)
en1 English Luckwet 2025-08-28 21:24:23 604 Initial revision (published)