All seated
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
properties?
Age
7 to 11
Challenge level
Problem
Found in the playground of a Danish school - something to sit on!
Image
What do you notice?
Can you make another square using the numbers $1$ to $16$, that displays the same properties?
Find out what Albrecht Dürer has to do with this arrangement of numbers.
There are twelve different types of $4$ by $4$ magic square that use the numbers $1$ to $16$. See if you can find information about these twelve types and show examples of each one.
Look carefully in each case at the patterns produced when a total of $17$ is searched for.
Can you finish off the $5$ by $5$ magic square below?
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$23$
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$6$
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$19$
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$2$
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$15$
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$10$
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$1$
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|||
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$5$
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$9$
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|||
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$4$
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$12$
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$8$
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||
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$11$
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$7$
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$3$
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Student Solutions
Mary sent us her solution:
If you add up the numbers in each row, in each column, and in each long diagonal, you always get the same answer. It's a magic square. Durer put a magic square in one of his pictures
Also, if you pick a number and look for 17 minus it, then look at other pairs that add up to 17, it's symmetrical.
The 5x5 magic square must be filled in like this (I did it one step at a time, seeing what was possible, and this was the only way that worked):
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23
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6 | 19 | 2 | 15 |
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10
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18 | 1 | 14 | 22 |
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17
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5 | 13 | 21 | 9 |
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4
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12 | 25 | 8 | 16 |
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11
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24 | 7 | 20 | 3 |