Stones on a grid puzzle
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From: Richard Heathfield on 11 Jun 2010 17:20 Carl G. wrote: > "Leroy Quet" <qqquet(a)mindspring.com> wrote in message > news:f6f2728d-cfb6-44bf-9a4a-b1401866a4d1(a)d37g2000yqm.googlegroups.com... >> Way to go! These two solutions are different than Rob Pratt's. So >> there are at least 3 solutions modulo rotations, reflections, and >> color reversals. >> >> I bet there are a lot of such solutions. >> >> Thanks, >> Leroy Quet >> > > I pleased to know that my intuition was way off! > > Next Challenge: Is there a solution with the products 1 to 9 all in the > row-products? I'll pass on that one for now, but... > I noticed that both diagonal products of Richard Heathfield's solution are > 3. What other matching diagonal products are possible? ....here's one with diagonal products 4 and 6: o x x x x x o x x 10 o o o o o o o x x 14 o o x o o x o x x 8 x o o o x o x o x 3 x o x o x o x o o 2 o o o o o o x o o 12 o x x x x x x x o 7 o o o x o o o x o 9 x x x x x o o x x 20 18 5 1 15 4 6 24 27 16 -- Richard Heathfield <http://www.cpax.org.uk> Email: -http://www. +rjh@ "Usenet is a strange place" - dmr 29 July 1999 Sig line vacant - apply within
From: Chip Eastham on 11 Jun 2010 18:15 On Jun 11, 5:20 pm, Richard Heathfield <r...(a)see.sig.invalid> wrote: > Carl G. wrote: > > "Leroy Quet" <qqq...(a)mindspring.com> wrote in message > >news:f6f2728d-cfb6-44bf-9a4a-b1401866a4d1(a)d37g2000yqm.googlegroups.com.... > >> Way to go! These two solutions are different than Rob Pratt's. So > >> there are at least 3 solutions modulo rotations, reflections, and > >> color reversals. > > >> I bet there are a lot of such solutions. > > >> Thanks, > >> Leroy Quet > > > I pleased to know that my intuition was way off! > > > Next Challenge: Is there a solution with the products 1 to 9 all in the > > row-products? > > I'll pass on that one for now, but... > > > I noticed that both diagonal products of Richard Heathfield's solution are > > 3. What other matching diagonal products are possible? > > ...here's one with diagonal products 4 and 6: > > o x x x x x o x x 10 > o o o o o o o x x 14 > o o x o o x o x x 8 > x o o o x o x o x 3 > x o x o x o x o o 2 > o o o o o o x o o 12 > o x x x x x x x o 7 > o o o x o o o x o 9 > x x x x x o o x x 20 > 18 5 1 15 4 6 24 27 16 > > -- > Richard Heathfield <http://www.cpax.org.uk> > Email: -http://www. +rjh@ > "Usenet is a strange place" - dmr 29 July 1999 > Sig line vacant - apply within I noticed your solutions all have the same _set_ of products, but it took me a bit to realize this is forced. Given that prime values greater than 9 are unattainable, as are 21, 22, 25, and 26, and that 27 is the largest attainable product, the only 18 distinct products attainable are those in the solutions shown: 1 through 10, 12, 14, 15, 16, 18, 20, 24, 27. regards, chip
From: Rob Pratt on 11 Jun 2010 17:17 "Carl G." <cginnowzerozeroone(a)microprizes.com> wrote in message news:koxQn.290$5N3.175(a)bos-service2b.ext.ray.com... > > "Leroy Quet" <qqquet(a)mindspring.com> wrote in message > news:f6f2728d-cfb6-44bf-9a4a-b1401866a4d1(a)d37g2000yqm.googlegroups.com... >> Way to go! These two solutions are different than Rob Pratt's. So >> there are at least 3 solutions modulo rotations, reflections, and >> color reversals. >> >> I bet there are a lot of such solutions. >> >> Thanks, >> Leroy Quet >> > > I pleased to know that my intuition was way off! > > Next Challenge: Is there a solution with the products 1 to 9 all in the > row-products? > > I noticed that both diagonal products of Richard Heathfield's solution are > 3. What other matching diagonal products are possible? > > Carl G. 1 to 9 in row products: 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 1 1 1 0 1 0 1 1 0 1 0 Rob Pratt
From: Leroy Quet on 12 Jun 2010 07:57 Let r = the sum of the row products, and let c be the sum of the column products. Let q = |c-r|. The solutions where 1 through 9 are all row products (or column products) maximizes q, obviously. Can anyone find a solution that gives the MINIMUM possible q, whatever that q is? Also, I am wondering if the 10-by-10 grid (and larger grids) would be easier or harder to solve than the 9-by-9 grid. Thanks, Leroy Quet
From: Richard Heathfield on 12 Jun 2010 09:18 Leroy Quet wrote: <snip hard bit :-) > > Also, I am wondering if the 10-by-10 grid (and larger grids) would be > easier or harder to solve than the 9-by-9 grid. I think they get harder. Here's a 14x14, which took me rather longer than I expected. I tried hard to get a 15x15, but haven't yet succeeded. o o o x x x o x o o o x x x 81 x o o o o o x x o x x x x o 40 o x o x o x x o o x x o o x 16 x o x o o x o x o x o x x o 4 o o x x o x x x o o o o o x 60 o o x o o x x o o o x o o o 72 o o o o x x x x o o o x o x 48 x x x o o x x x x o o o x x 144 o x x x x x x x o o x x x x 56 x x o o o o o x x x x o o x 80 o x x o o x x x o o o o x x 96 x o o o x x o x x x x x o x 30 o x o x o o o x x o o o x x 36 o x o o x x x o x x o x o o 24 6 64 54 9 10 14 20 28 21 15 32 8 12 7 For anything bigger than this, I think I'd probably give in and write a program! -- Richard Heathfield <http://www.cpax.org.uk> Email: -http://www. +rjh@ "Usenet is a strange place" - dmr 29 July 1999 Sig line vacant - apply within
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