[seqfan] Re: Packing many different square sizes in a square

Giovanni Resta g.resta at iit.cnr.it
Wed Jun 19 10:38:52 CEST 2013


On 06/18/2013 06:31 PM, Allan Wechsler wrote:

> Up to n=16, the answer seems to be ceiling(n/2), but I cannot pack 9
> different square sizes on a 17x17 board.  The sequence I have so far is
>
> 1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,8,9,9,9
>
> and if this is right, it's not in OEIS yet. Can any sequence fanatic
> increase any of these numbers?  Or give more terms?

I got these terms, for n=1,..,33.

1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 
10, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14

I've attached the packing for n=33 which so far is the most "dense"
one, in the sense that the ratio between number of unit squares and 
total area is the smallest.

Giovanni


More information about the SeqFan mailing list