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        riddles >> hard >> 11 Digit Numbers
        
(Message started by: K_Sengupta on Nov 21^st, 2005, 12:18am)

Title: 11 Digit Numbers
Post by K_Sengupta on Nov 21^st, 2005, 12:18am

Place the digits 1,2,3,5,6,7, 8, 9 in a 11x11 Square Board with each of the eight digits occurring at least once but not repeated more than four times in any row or any column such that:

(i) All the 11 digit numbers constituted by reading each row from left to right or by reading each row from right to left are prime numbers.

(ii) All the 11 digit numbers arising out of the columns are Palindromes.

(iii) No two out of the of eleven 11-digit numbers arising out of the columns (reading only up-down ) are equal.

(iv) The twelve 11-digit numbers arising out of the first six rows ( reading both right-left and left-right) are all distinct.

Title: Re: 11 Digit Numbers
Post by Barukh on Nov 21^st, 2005, 12:51am

I am confused about the conditions... Aren't (ii) and (iii) contradictory?

Because of (ii), SB[1, j] = SB[11, j] for every j = 1, ..., 11. But that means SB[1] = SB[11], contradicting (iii).

Am I missing something? :-/

Title: Re: 11 Digit Numbers
Post by K_Sengupta on Nov 21^st, 2005, 11:08pm

The precise meaning of Clause (iii) is :
(a) No pairs of 11 digit numbers considering all the eleven of the said numbers with each of the said numbers arising out of each of the columns
( since reading up- down and reading down-up are identical in this case since there are only eleven distinct numbers in this case instead of 22 eleven digit numbers in case the palindrome restriction
was not imposed) are identical and
(b) No two eleven digit numbers among the 22 available eleven digit numbers arising out of any two given rows are identical.
However to avoid any further confusion, I am incorporating some very minor amendments only in the language corresponding to clause (III ) of my original problem.

Title: Re: 11 Digit Numbers
Post by Grimbal on Nov 22^nd, 2005, 2:43am

Still, if the columns are palindromes, the top row must equal the bottom row.

Title: Re: 11 Digit Numbers
Post by K_Sengupta on Nov 25^th, 2005, 9:51pm

I confirm having suitably amended the body of the problem.