place-1-25-in-table-5-5-in-such-away-that-the-sum-is-constant-in-all-directions-direction-

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

$${place}\left(\mathrm{1}\rightarrow\mathrm{25}\right) \\ $$$${in}\:{table}\left(\mathrm{5}×\mathrm{5}\right){in}\:{such}\:{away}\:{that} \\ $$$${the}\:{sum}\:{is}\:{constant}\:{in}\:{all}\:{directions}. \\ $$$$\left[\:\mid\underset{−} {\overset{−} {×}}\mid\:\right]\rightarrow\left({direction}\right) \\ $$

Commented by esmaeil last updated on 02/Jan/24

$${for}\:{example}\:\left(\mathrm{3}×\mathrm{3}\right) \\ $$$$\:\:\:\left[\mathrm{8}\right]\:\:\:\left[\mathrm{1}\right]\:\:\:\:\left[\mathrm{6}\right] \\ $$$$\:\:\:\left[\mathrm{3}\right]\:\:\:\left[\mathrm{5}\right]\:\:\:\:\left[\mathrm{7}\right] \\ $$$$\:\:\:\left[\mathrm{4}\right]\:\:\:\left[\mathrm{9}\right]\:\:\:\:\left[\mathrm{2}\right] \\ $$

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

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{65} \\ $$$$\begin{array}{|c|c|c|c|c|c|}{\mathrm{17}}&\hline{\mathrm{24}}&\hline{\mathrm{1}}&\hline{\mathrm{8}}&\hline{\mathrm{15}}&\hline{\mathrm{65}}\\{\mathrm{23}}&\hline{\mathrm{5}}&\hline{\mathrm{7}}&\hline{\mathrm{14}}&\hline{\mathrm{16}}&\hline{\mathrm{65}}\\{\mathrm{4}}&\hline{\mathrm{6}}&\hline{\mathrm{13}}&\hline{\mathrm{20}}&\hline{\mathrm{22}}&\hline{\mathrm{65}}\\{\mathrm{10}}&\hline{\mathrm{12}}&\hline{\mathrm{19}}&\hline{\mathrm{21}}&\hline{\mathrm{3}}&\hline{\mathrm{65}}\\{\mathrm{11}}&\hline{\mathrm{18}}&\hline{\mathrm{25}}&\hline{\mathrm{2}}&\hline{\mathrm{9}}&\hline{\mathrm{65}}\\{\mathrm{65}}&\hline{\mathrm{65}}&\hline{\mathrm{65}}&\hline{\mathrm{65}}&\hline{\mathrm{65}}&\hline{\mathrm{65}}\\\hline\end{array} \\ $$$$\:\mathrm{65}\:{are}\:{sums}\:{of}\:{rows} \\ $$$$\mathrm{65}\:{are}\:{sums}\:{of}\:{columns} \\ $$$$\mathrm{65}\:{are}\:{sums}\:{of}\:{diagonals} \\ $$

Commented by esmaeil last updated on 02/Jan/24

$$\:\cancel{\lesseqgtr} \\ $$

Commented by esmaeil last updated on 02/Jan/24

$${it}\:\:{can}\:{be}\:{solved}\:{for}\:{all}\:{tables} \\ $$$${with}\:{odd}\:{number}\:{of}\:{rows}\:\:{and} \\ $$$${columns}. \\ $$

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

$$\mathcal{A}{lso}\:{for}\:{even}\:{order}\:{there}\:{are}\:{different} \\ $$$${patterns}/{rules}. \\ $$

Answered by BaliramKumar last updated on 02/Jan/24

Commented by BaliramKumar last updated on 02/Jan/24

$$\mathrm{write}\:\mathrm{1}\:\mathrm{to}\:\mathrm{25}\:\mathrm{continuous}\:\mathrm{and}\:\mathrm{fit}\:\mathrm{same}\:\mathrm{colour}\:\mathrm{box} \\ $$$$\mathrm{start}\:\mathrm{any}\:\mathrm{number} \\ $$$$\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\mathrm{5},\:………\:\mathrm{24},\mathrm{25},\:\mathrm{1} \\ $$$$\mathrm{10},\mathrm{11},\mathrm{12},\:\mathrm{13},\:………\:\mathrm{24},\mathrm{25},\:\mathrm{1}\:……..\mathrm{8},\:\mathrm{9} \\ $$$$ \\ $$

Commented by esmaeil last updated on 02/Jan/24

$${clever}\:{solution}. \\ $$$${excellent} \\ $$

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