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        riddles >> hard >> 12 DIGIT NUMBERS
        
(Message started by: K Sengupta on Nov 27^th, 2005, 11:24pm)

Title: 12 DIGIT NUMBERS
Post by K Sengupta on Nov 27^th, 2005, 11:24pm

Place the digits 1,2,3,4,5,6,7,8 and 9 in a 12x12 Square Board with each of the nine digits occurring at least once but not repeated more than three times in any row or any column and all the twenty four 12 Digit Numbers arising out of the rows (reading both left-right and right-left) are different while all the twenty four 12-Digit numbers arising out of the columns (reading both down-up and up-down ) are distinct such that :

(a) All the twenty four 12 Digit Numbers constituted by reading the rows both left-right and right-left are Prime Numbers.

(b) All the twelve 12 Digit Numbers constituted by reading the columns only up-down are in Arithmetic Progression while reading the columns in a down-up manner generates a different Arithmetic Series comprising twelve 12 Digit Numbers.

Would there exist any solution to this problem if Clause-(b) were amended in the following manner?

"(b): All the twelve 12 digit numbers constituted by
reading the columns only up-down describes a Harmonic Series?"