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Timeline for 1 rectangle <= 4 squares

Current License: CC BY-SA 2.5

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Mar 7, 2010 at 22:44 comment added TonyK I can confirm your latest result for the 12x1 rectangle in a 241x126 grid. (And the first five rows are all zero, so the grid is really 231x126.) 181/48 = 3.7708333...! That's more than 3.75, isn't it? :-)
Mar 4, 2010 at 8:08 comment added TonyK Given that 7x1 was no improvement on 6x1, perhaps it might be worth trying 14x1 or 15x1.
Mar 4, 2010 at 7:38 comment added TonyK And I can confirm your 155x68 result too.
Mar 4, 2010 at 0:31 history edited F_G CC BY-SA 2.5
1x12 -> 3.75 result; deleted 1 characters in body
Mar 3, 2010 at 21:54 comment added TonyK I can confirm your new 15/4 result for the 12x1 rectangle. (And your first two rows are all zero, so the rectangle is really 157x82.)
Mar 3, 2010 at 13:49 comment added Yaakov Baruch I can confirm the 101/27 result. I also checked the real case (no surprises) and I'm updating the related post.
Mar 3, 2010 at 12:27 history edited F_G CC BY-SA 2.5
New 3.7407407 sum
Mar 3, 2010 at 11:53 comment added Yaakov Baruch the update is impressive. Shouldn't it be part of an update to the main question itself?
Mar 3, 2010 at 11:14 history edited F_G CC BY-SA 2.5
added 336 characters in body
Mar 2, 2010 at 21:27 comment added TonyK I can confirm that FG's 3x7 solution attains 56/15. Well done!
Mar 2, 2010 at 20:43 history edited F_G CC BY-SA 2.5
deleted 3 characters in body
Mar 2, 2010 at 20:15 history answered F_G CC BY-SA 2.5