#### chris84567

##### New member

- Joined
- Jan 23, 2018

- Messages
- 12

Not sure if this is the correct category, if its not sorry.

If you create a 3x3 grid of unique integers squared, each row, column and diagonal has to be equal to N.

What is one solution to this problem and what is a general solution to this problem?

Using systems of equtions I was able to find that e[SUP]2[/SUP]= 1/3n.

a[SUP]2 [/SUP]+b[SUP]2 [/SUP]+c[SUP]2 [/SUP]=n

-(a[SUP]2 [/SUP]+e[SUP]2 [/SUP]+i[SUP]2 [/SUP]=n)

-(b[SUP]2 [/SUP]+e[SUP]2 [/SUP]+h[SUP]2 [/SUP]=n)

-(c[SUP]2 [/SUP]+e[SUP]2 [/SUP]+g[SUP]2 [/SUP]=n)

g[SUP]2 [/SUP]+h[SUP]2 [/SUP]+i[SUP]2 [/SUP]=n

=

-3e[SUP]2 [/SUP]=n

After this I have been able to write everything in terms of a, c and n but don't know where to go next.

Thanks for any help you can offer.

If you create a 3x3 grid of unique integers squared, each row, column and diagonal has to be equal to N.

What is one solution to this problem and what is a general solution to this problem?

n | |||

a[SUP]2[/SUP] | b[SUP]2[/SUP] | c[SUP]2[/SUP] | n |

d[SUP]2[/SUP] | e[SUP]2[/SUP] | f[SUP]2[/SUP] | n |

g[SUP]2[/SUP] | h[SUP]2[/SUP] | i[SUP]2[/SUP] | n |

n | n | n | n |

Using systems of equtions I was able to find that e[SUP]2[/SUP]= 1/3n.

a[SUP]2 [/SUP]+b[SUP]2 [/SUP]+c[SUP]2 [/SUP]=n

-(a[SUP]2 [/SUP]+e[SUP]2 [/SUP]+i[SUP]2 [/SUP]=n)

-(b[SUP]2 [/SUP]+e[SUP]2 [/SUP]+h[SUP]2 [/SUP]=n)

-(c[SUP]2 [/SUP]+e[SUP]2 [/SUP]+g[SUP]2 [/SUP]=n)

g[SUP]2 [/SUP]+h[SUP]2 [/SUP]+i[SUP]2 [/SUP]=n

=

-3e[SUP]2 [/SUP]=n

After this I have been able to write everything in terms of a, c and n but don't know where to go next.

n | |||

a[SUP]2[/SUP] | b[SUP]2[/SUP] | c[SUP]2[/SUP] | n |

d[SUP]2[/SUP] | [SUP]1n/3[/SUP] | f[SUP]2[/SUP] | n |

g[SUP]2[/SUP] | h[SUP]2[/SUP] | i[SUP]2[/SUP] | n |

n | n | n | n |

Thanks for any help you can offer.

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