3 items are filed under this topic.








Magic squares 
20011117 

From A student: 7th grader wanting to find solution to magic square:
place the integers from 5 to +10 in the magic square so that the total of each row, column, and diagonal is 10. The magic square is 4 squares x 4 squares. Answered by Penny Nom. 





Pythagoras & magic squares 
20011009 

From John: My grandson became intrigued when he recently 'did' Pythagoras at elementary school. He was particularly interested in the 345 triangle, and the fact that his teacher told him there was also a 51213 triangle, i.e. both rightangled triangles with whole numbers for all three sides. He noticed that the shortest sides in the two triangles were consecutive odd numbers, 3 & 5, and he asked me if other right angled triangles existed, perhaps 'built' on 7, 9, 11 and so on. I didn't know where to start on this, but, after trying all sorts of ideas, we discovered that the centre number in a 3order 'magic square' was 5, i.e. (1+9)/2, and that 4 was 'one less'. Since the centre number in a 5order 'magic square' was 13 and that 12 was 'one less' he reckoned that he should test whether a 7order square would also generate a rightangled triangle for him. He found that 72425, arrived at by the above process, also worked! He tried a few more at random, and they all worked. He then asked me two questions I can't begin to answer ...  Is there a rightangled triangle whose sides are whole numbers for every triangle whose shortest side is a whole odd number? and
 Is each triangle unique (or, as he put it, can you only have one wholenumbersided rightangled triangle for each triangle whose shortest side is an odd number)?
Answered by Chris Fisher. 





Magic Squares 
19990211 

From Katie Powell: My name is Katie Powell. I'm in the 7th grade, taking Algebra. I live in Houston, Texas. My problem is this: "Use the numbers 19 to fill in the boxes so that you get the same sum when you add vertically, horizontally or diagonally." The boxes are formed like a tictactoe  with 9 boxes  3 rows and 3 columns. Can you help? Answered by Jack LeSage. 


