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Level 3. Fractional Magic Squares Tui has begun to like magic squares. She decided to make all of the magic squares that she could using the numbers 2.0, 2.2, 2.4, 2.6 and 2.8. How many could she make if she used each number at least once in the square?

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## Level 3

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**Level 3**• Fractional Magic Squares • Tui has begun to like magic squares. She decided to make all of the magic squares that she could using the numbers 2.0, 2.2, 2.4, 2.6 and 2.8. How many could she make if she used each number at least once in the square? • It took her quite a while because she didn’t know that the sum of a magic square was always three times the number in the centre.**Level 3**• Big Magic Squares • Tui has begun to like magic squares. She decided to make all of the magic squares that she could using the numbers 222, 555 and 888. How many could she make if she used each number at least once in the square? • It took her quite a while because she didn’t know that the sum of a magic square was always three times the number in the centre.**Level 4**• Negative Magic Squares • Tui has begun to really like magic squares. She decided to make all of the magic squares that she could using the numbers –2, 4 and 10 down the main diagonal. How many can she make? • It took her quite a while because she didn’t know that the sum of a magic square was always three times the number in the centre.**Level 4**• Fractional Magic Squares • Tui has really begun to get the idea of magic squares. She decided to make all of the magic squares that she could using the fractions 7/6, 4/3 3/2. How many can she make? • It took her quite a while because she didn’t know that the sum of a magic square was always three times the number in the centre.**Level 5**• The Magic Squares • Tui has realised that there are nine positions in a magic square. So can she make up a magic square using each of the numbers 1, 2, 3, 4, 5, ,6, 7, 8, 9 once and only once?**Level 6!**• Difference Magic Squares: • Tui has become pretty well exhausted by magic squares. But she decides to have one more try but with a twist. • She wonders if it is possible to place the numbers 1 through to 9 in a 3 by 3 grid, so that in any direction of three squares (across, down or diagonally) the sum of the first and last numbers minus the centre number gives the same answer. • If it is possible, how many different answers exist?

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