The New Sudoku Players' Forum

by **udosuk** » Fri Apr 28, 2006 10:34 pm

Great job mates (particularly Ruud)!

I got 18, so 2 more for you guys & gals to discover...

But there could be more that I haven't realised...

Anyway you could try to list out the "area ratio" of each configuration, e.g.: 1,1,1,1 or 1,3,12,48...

by **emm** » Fri Apr 28, 2006 11:19 pm

Edit : Asked and answered my own question.

by **Ruud** » Fri Apr 28, 2006 11:54 pm

OK thanks, nice to know the target. 17 :!:

One more to go

Ruud.

by **udosuk** » Sun Apr 30, 2006 12:18 pm

Is anybody still looking for the eluding #18? :?:

Tell me when you would like me to reveal my answer...

by ab » Sun Apr 30, 2006 3:22 pm

I've spent ages looking at the 17 found so far for inspiration. I'd be happy if you'd put me outta my misery.

Great problem BTW

by **udosuk** » Sun Apr 30, 2006 3:38 pm

The truth is, you probably could not find any significant inspiration by merely looking at the previous 17 configurations... But #17 (from Ruud) could give some slight glimpse of hope, especially if you can guess how Ruud came up with that...

In fact I thought Ruud could have nailed it when he found #17 since #17 & #18 are normally found together...

Anyway I'll wait one more day and preferably with Ruud's formal approval to show the final one out... Or if somebody can work it out from my hints above...

by **ronk** » Sun Apr 30, 2006 9:25 pm

by **udosuk** » Mon May 01, 2006 3:18 am

That's it. Well done ronk.

I doubt a #19 exists... :?:

by **udosuk** » Mon May 01, 2006 9:06 am

Some graphics done by me...

Bi-cutting 3,4,9
#01: 9,12,16,27
#02: 3,9,16,36
#03: 1,3,3,9 (a)

Bi-cutting 1,3,12
#03: 1,3,3,9 (a) (duplicated)
#04: 3,4,9,48
#05: 1,3,12,48

Bi-cutting 1,1,1
#06: 1,3,4,4 (a)
#07: 1,3,4,4 (b)
#08: 1,3,4,4 (c)

Tri-cutting 1,3
#09: 1,1,1,1 (a)
#10: 1,1,1,9

Flipping rectangle of 1,3,3,9 (a)
#11: 1,3,3,9 (b)

Rotating equilateral triangle of 1,1,1,1 (a)
#12: 1,1,1,1 (b)
#13: 1,1,1,1 (c)

Flipping rectangle of 1,1,1,1 (b)
#14: 1,1,1,1 (d)

Tri-cutting 30-30-120 triangle of 1,2
#15: 1,1,3,4 (a)
#16: 1,1,3,4 (b)

triangle within triangles
#17: 1,4,4,16
#18: 9,12,12,16

I deliberately tried to make good approximation to the 30-60-90 triangles...
I regarded 15-26-30 as the best "unit" side ratio...

by **underquark** » Mon May 01, 2006 9:41 pm

If that's it for 4 (and it certainly looks and "feels" right) then what about 5? Once that is answered it ought to possible to conjecture a series or proof for 6, 7, 8 etc.

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Triangle cutting problem