[Magictour] Re: Bounds

JC wrote:

>I would like to talk about bounds.
>As I previously explained, for high bounds, I used
>260,260-64,260-64-62,etc... (in my previous mail, I made a typo by using
>196-64 instead of 260-64, etc...)
>
>My question is: can we obtain better bounds ?
>
>With 4 empty squares, the optimal pattern is:
>
>64 00 62 00 60 00 58 <- this line contains the sum 64+62+60+58
>00 00 00 00 00 00 00
>00 63 00 61 00 59 00

I can complete this :

64 07 62 05 60 03 58 01
00 00 00 00 00 00 00 00
08 63 06 61 04 59 02 57


but are you starting with 64 ?
Completable means to me, that the empty squares can be filled later
with numbers bigger than the largest number in the row.


>What are the highest possible sums on one line with 3, 2 and 1 empty
squares
>?
>
>Solving this question will solve the following question (by using the 65
>complement of every square) :
>What are the lowest possible sums on one line with 3, 2 and 1 empty squares
>?

to solve(approximate) it numerically,
you could try to generate all SMKTs where you ignore the sums of the columns
and then find the maxima with 3,2,1 of all their rows.
It should be sufficient to generate a lot random such {rows=260}-tours

>Improving these values will allow us to search for a 8x10 magic rectangle
>(this time, the computation will be distributed !).

do you have an estimate, how long it will take ?


Guenter


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Received on Thu Dec 04 14:24:18 2001