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Subject: Re: Number of six men tablebases.

Author: Phil Dixon

Date: 14:28:30 08/09/99

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On August 09, 1999 at 16:14:13, Bruce Moreland wrote:

>
>On August 09, 1999 at 15:29:44, blass uri wrote:
>
>>
>>On August 09, 1999 at 13:46:37, José de Jesús García Ruvalcaba wrote:
>>
>>>	I finally sat down and make all the computations from scratch and then
>>>rechecked the results.
>>>Number of 5+1 tablebases: 40
>>>Number of 4+2 tablebases: 200
>>>Number of 3+3 tablebases: 120
>>>Total number of six men tablebases: 360
>>>	If there is interest I can explain how I got the results, they are simple
>>>combinatorics problems.
>>>José.
>>Your calculation is wrong.
>>For example the first number is 70
>>
>>if I represent  P=1,N=2,B=3,R=4,Q=5 then the I can represent every 5+1 material
>>configuration(4+0 without kings) as 4 numbers and the number of possible
>>configuration is 70
>>
>>I can represent pppp configuration by 1111
>>pppn by 1112 pppb by 1113
>>
>>You can count non decreasing sequence of 4 numbers(out of numbers 1,2,3,4,5)
>>1111 1112 1113 1114 1115
>>1222 1223 1224 1225 1233
>>1234 1235 1244 1245 1255
>>1333 1334 1335 1344 1345
>>1355 1444 1445 1455 1555
>>2222 2223 2224 2225 2233
>>2234 2235 2244 2245 2255
>>2333 2334 2335 2344 2345
>>2355 2444 2445 2455 2555
>>
>>are only 45 options.
>>
>>You can translate every non decreasing sequence by adding 1 to the second
>>number, adding 2 to the 3th number and adding 3 to the 4th number.
>>
>>The problem is how many increasing sequences you can choose from the numbers 1-8
>> and the answer is 8!/(4!*4!)=70
>>
>>
>>Uri
>
>By my count, there are 5 3-man databases, 30 4-man databases, 110 5-man
>databases, 365 6-man databases, and 1001 7-man databases.
>
>bruce

Is it possible to generate a six-man tablebase with pawns in a reasonable amount
of time?   Will there be one someday?  Is anyone working on it?

Regards,
Phil



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