Perhaps you've seen the magic square
8 1 6
3 5 7
4 9 2
which has the property that all rows, columns and diagonals sum to 15. Well, it has another "magic" and "square" property! If you read the rows as NUMBERS, forwards and backwards, and square them, then
8162 + 3572 + 4922 = 6182 + 7532
+ 2942.
Magic?
Presentation Suggestions:
If they like this fun fact, ask them to take a minute to see what happens with
the columns. Then try the "diagonals" which wrap around the square...
The Math Behind the Fact:
This holds for ANY 3x3 magic squares (though if the entries contain more than
one digit, you will have to carry the extra places) using techniques of linear
algebra. For instance, for this magic square:
13 6 11
8 10 12
9 14 7
you can check that:
(1300+60+11)2 +(800+100+12)2 +(900+140+7)2 =
(1100+60+13)2 +(1200+100+8)2 + (700+140+9)2.