MAGIC SQUARES

© '96 John Knoderer
www.MAZES.com - P O Box 235 - Sulphur Springs AR 72768 USA

The numbers in a magic square add up to the same sum in several ways:

Every row adds up to the same number
Every column adds up to that same number
Both diagonals add up to that number
The four corners add up to that number
The four middle squares add up to that number
The four squares in the top left corner add up to that number
The four squares in the top right corner add up to that number
The four squares in the bottom left corner add up to that number
The four squares in the bottom right corner add up to that number

Each number in the list will only be used once, and every number will be used. In the puzzles below, there is only one solution to each set of numbers. A magic square is NOT NECESSARILY a perfect square.

This is a magic square:

Magic Square
7 6 12 9 10 11 5 8 13 16 2 3 4 1 15 14

Just in case your browser doesn't support tables, here's a second copy of the above:

+--+--+--+--+
| 7| 6|12| 9|
+--+--+--+--+
|10|11| 5| 8|
+--+--+--+--+
|13|16| 2| 3|
+--+--+--+--+
| 4| 1|15|14|
+--+--+--+--+

PERFECT SQUARES

The numbers in a perfect square add up to the same sum in many ways:

Every row, every column, and every diagonal add up to that number
The four corners add up to that number
Every neighboring four numbers (in a 2x2 block) add up to that number
If you take the bottom row off the bottom and attach it to the top, it will still be a perfect square
If you take the column off the left, and put it on the right, it will still be a perfect square

This is a perfect square:

Perfect Square
1 15 6 12 8 10 3 13 11 5 16 2 14 4 9 7

Just in case your browser doesn't support tables, here's a second copy of the above:

+--+--+--+--+
| 1|15| 6|12|
+--+--+--+--+
| 8|10| 3|13|
+--+--+--+--+
|11| 5|16| 2|
+--+--+--+--+
|14| 4| 9| 7|
+--+--+--+--+

Find these MAGIC SQUARES

Here are nine more MAGIC SQUARES to find:

(if you are given a list of sequential numbers, but not the sum, the sum will be equal to (first+last)*2, or in the case of the first puzzle, (83+98)*2=362, in the case of the second puzzle, (5+35)*2=80.)

three easy MAGIC SQUARE puzzles

Only a calculator will be needed for easy puzzles

1. Use every number    2. Use every odd number  3. Use every fourth #
   from 83 to 98          from 5 to 35             from 28 to 88
   (all sums are 362)     (all sums are 80)        (all sums are ???) 

   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |89|  |  |  |          |33|15|  |  |            |48|40|  |76|
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |92|93|  |  |          |  | 5|  |  |            |84|  |  |56|
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |  |98|84|  |          |  |35|  |  |            |  |52|  |  |
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |86|  |  |  |          | 7|  |  |31|            |  |  |  |  |
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+

three harder MAGIC SQUARE puzzles

some thinking or trial-and-error may be required

4. Use every number   5. Use every third #      6. Use every fourth #
   from 61 to 76          from 10 to 55            from 21 to 81
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |  |  |  |66|          |25|  |  |34|            |  |  |  |  |
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |  |  |  |  |          |  |  |  |  |            |53|37|33|  |
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |  |69|  |72|          |  |31|  |13|            |  |73|  |  |
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |64|  |  |73|          |  |  |  |55|            |  |  |  |57|
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+

three hardest MAGIC SQUARE puzzles

the most thinking will be required for these hardest puzzles

7. Use every even #    8. Use every fifth #     9. Use every ?? number
   from 32 to 62          from ?? to ??            from ?? to ??
   (all sums = ???)       (all sums = 230)         (all sums = 270)
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |42|62|32|  |          |80|  |  |  |            |68|  |  |  |
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |  |  |  |  |          |  |65|  |  |            |  |  |  |  |
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |  |  |  |  |          |  |  |  |  |            |  |  |  |  |
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |  |38|  |  |          |25|95|  |  |            |71|60|  |65|
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+

Find these PERFECT SQUARES

Here are nine more PERFECT SQUARES to find:

three easy PERFECT SQUARE puzzles

1. Use every fourth #  2. Use every number      3. Use every number
   from 21 to 81          from 72 to 87            from 18 to 33
   (all sums are 362)     (all sums are ???)       (all sums are ???) 
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |  |  |  |29|          |  |  |  |  |            |  |  |  |  |
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |25|45|  |  |          |  |73|  |  |            |  |  |  |30|
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |61|  |33|  |          |  |78|83|72|            |  |22|  |19|
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |  |  |  |  |          |  |  |  |86|            |  |  |26|24|
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+

three harder PERFECT SQUARE puzzles

4. Use every third #   5. Use every even #      6. Use every fourth #
   from 37 to 82          from 18 to 48            from 5 to 65
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |  |  |  |  |          |  |  |  |24|            |  |  |  |13|
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |  |76|46|61|          |  |32|38|26|            |  |  |  |  |
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |  |  |  |82|          |  |  |  |  |            |  |57|  |37|
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |  |  |  |  |          |  |  |  |  |            |  |  |49|  |
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+

three hardest PERFECT SQUARE puzzles

7. Use every even #    8. Use every fifth #     9. Use every ?? number
   from 32 to 62          from ?? to ??            from ?? to ??
   (all sums = ???)       (all sums = 230)         (all sums = 270)
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |  |  |  |  |          |  |  |21|  |            |  |  |  |22|
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |48|  |42|  |          |  |45|  |  |            |  |  |28|  |
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |  |45|  |  |          |  |  |33|  |            |  |  |  |40|
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+
   |  |  |  |  |          |  |  |  |  |            |  |  |  |  |
   +--+--+--+--+          +--+--+--+--+            +--+--+--+--+