Magic Error
Two of the numbers in a 4x4 magic square have been swapped. Can you work out the sum of these numbers?
Age
11 to 14
Challenge level
Problem
Two numbers in the 4 x 4 grid can be swapped to create a Magic Square (in which all rows, all columns and both main diagonals add to the same total).
What is the sum of these two numbers?
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Student Solutions
Answer: 13 + 15 = 28
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Rows should all be the same
$\therefore$ all 34
$\therefore$ second and bottom each need to change by 2
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Either swap 10, 12,
or swap 13, 15
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Columns should also all be 34
$\therefore$ second column sum needs to increase
Swap 13 and 15
13 + 15 = 28