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3 items are filed under this topic.
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Magic squares |
2001-11-17 |
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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. |
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Pythagoras & magic squares |
2001-10-09 |
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From John:
My grandson became intrigued when he recently 'did' Pythagoras at elementary school. He was particularly interested in the 3-4-5 triangle, and the fact that his teacher told him there was also a 5-12-13 triangle, i.e. both right-angled 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 3-order 'magic square' was 5, i.e. (1+9)/2, and that 4 was 'one less'. Since the centre number in a 5-order 'magic square' was 13 and that 12 was 'one less' he reckoned that he should test whether a 7-order square would also generate a right-angled triangle for him. He found that 7-24-25, 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 right-angled 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 whole-number-sided right-angled triangle for each triangle whose shortest side is an odd number)?
Answered by Chris Fisher. |
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Magic Squares |
1999-02-11 |
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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 1-9 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 tic-tac-toe -- with 9 boxes -- 3 rows and 3 columns. Can you help?
Answered by Jack LeSage. |
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