# [seqfan] Re: Unique Products Regarding Binary Matrices

Rick Shepherd rlshepherd2 at gmail.com
Fri Jun 11 21:09:07 CEST 2010

```Thanks, Rob, for saving me/us some thinking ( :^J).

A small side-question of possible interest:
Does a solution exist such that flipping the bits on only *one* row (equiv.,
column) just rearranges the products for the columns (equiv., row) -- giving
another solution?

(I haven't even attempted that fully with your solution yet although I do
confirm that you have a solution.)

Thanks,
Rick

On Fri, Jun 11, 2010 at 2:34 PM, Rob Pratt <Rob.Pratt at sas.com> wrote:

> 18:
>
> 0    0    0    0    0    1    1    1    1
> 0    0    1    0    0    0    0    0    1
> 0    0    0    0    0    0    0    1    1
> 0    1    0    1    0    1    1    1    0
> 0    1    0    1    0    1    0    1    0
> 1    1    0    1    0    1    1    1    0
> 0    0    0    1    1    1    0    1    0
> 0    0    0    0    1    0    1    0    1
> 0    0    0    0    1    0    0    1    0
>
> Note that for n = 9, there are exactly 18 possible products (the ones you
> list below, and 1), so each one must be used.
>
> Rob
>
> -----Original Message-----
> From: seqfan-bounces at list.seqfan.eu [mailto:seqfan-bounces at list.seqfan.eu]
> On Behalf Of Douglas McNeil
> Sent: Friday, June 11, 2010 11:57 AM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: Unique Products Regarding Binary Matrices
>
>  > I too have been able to get 16 unique products. But getting those last
> 2 products to differ is a *little* tricky, perhaps, if possible.
>
> I can get 17 -- set([2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18,
> 20, 24, 27]) -- but not 18 yet.
>
>
> Doug
>
> --
> Department of Earth Sciences
> University of Hong Kong
>
>
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```