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Question Number 202750 by esmaeil last updated on 02/Jan/24

place(1→25)  in table(5×5)in such away that  the sum is constant in all directions.  [ ∣×_− ^− ∣ ]→(direction)

place(125)intable(5×5)insuchawaythatthesumisconstantinalldirections.[×](direction)

Commented by esmaeil last updated on 02/Jan/24

for example (3×3)     [8]   [1]    [6]     [3]   [5]    [7]     [4]   [9]    [2]

forexample(3×3)[8][1][6][3][5][7][4][9][2]

Answered by Rasheed.Sindhi last updated on 02/Jan/24

                                                  65   determinant (((17),(24),1,8,(15),(65)),((23),5,7,(14),(16),(65)),(4,6,(13),(20),(22),(65)),((10),(12),(19),(21),3,(65)),((11),(18),(25),2,9,(65)),((65),(65),(65),(65),(65),(65)))   65 are sums of rows  65 are sums of columns  65 are sums of diagonals

6517241815652357141665461320226510121921365111825296565656565656565aresumsofrows65aresumsofcolumns65aresumsofdiagonals

Commented by esmaeil last updated on 02/Jan/24

 ⋛

Commented by esmaeil last updated on 02/Jan/24

it  can be solved for all tables  with odd number of rows  and  columns.

itcanbesolvedforalltableswithoddnumberofrowsandcolumns.

Commented by Rasheed.Sindhi last updated on 02/Jan/24

Also for even order there are different  patterns/rules.

Alsoforevenordertherearedifferentpatterns/rules.

Answered by BaliramKumar last updated on 02/Jan/24

Commented by BaliramKumar last updated on 02/Jan/24

write 1 to 25 continuous and fit same colour box  start any number  2, 3, 4, 5, ......... 24,25, 1  10,11,12, 13, ......... 24,25, 1 ........8, 9

write1to25continuousandfitsamecolourboxstartanynumber2,3,4,5,.........24,25,110,11,12,13,.........24,25,1........8,9

Commented by esmaeil last updated on 02/Jan/24

clever solution.  excellent

cleversolution.excellent

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