Desired Number: -1728

-1728-424.5 -438.5 -437.5 -427.5 -1728-435.5 -429.5 -430.5 -432.5 -1728-431.5 -433.5 -434.5 -428.5 -1728-436.5 -426.5 -425.5 -439.5 -1728-1728 -1728 -1728 -1728 -1728

-1728-439.5 -425.5 -426.5 -436.5 -1728-428.5 -434.5 -433.5 -431.5 -1728-432.5 -430.5 -429.5 -435.5 -1728-427.5 -437.5 -438.5 -424.5 -1728-1728 -1728 -1728 -1728 -1728

For a complete discussion of Magic Squares, visit:http://www.mrexcel.com/tip069.shtml

Desired Number: 45Decimal Result 3.75

INTERMEDIATE RESULT 42 Integer Result 318 4 5 15 42 Shortage 37 13 12 10 4211 9 8 14 426 16 17 3 4242 42 42 42 42

FINAL RESULT 4518 4 8 15 4510 13 12 10 4511 12 8 14 456 16 17 6 4545 45 45 45 45

MAGIC SQUARES

STEP 1 15 1 2 12 304 10 9 7 308 6 5 11 303 13 14 0 30

30 30 30 30

STEP 2 18 4 5 15 427 13 12 10 42

11 9 8 14 426 16 17 3 42

42 42 42 42

Desired Number: 45 Enter a Total and see the effect

45

STEP 3 18 4 8 15 4510 13 12 10 4511 12 8 14 456 16 17 6 45

45 45 45 45 45Start number: 3Increment: 3

Enter numbers 0 to 15 starting at the Top left box and moving down one line at each row end. If the box is on a diagonal (marked RED) transpose the number to the opposite box (L to R and Top to Bottom). This gives a Magic Square with the row and columns totalling 30.

If you want a different total (between 30 and 100), you need to start at a different number. For example, for a total of 38, the start number is 2. For 42, the start number is 3 etc.

For totals between each increment of 4, the yellow boxes are incremented too, the amount depending on the remaining fraction after dividing the (Total minus 30) by 4. E.g. a total of 65 leaves 35 (i.e. 65 - 30). 35/4 = 8 Remainder 3. This adds 8 to the start number and increments the numbers in the yellow boxes by 3.

NOTE: The yellow boxes are the 1st and the boxes containing the next 3 counting in 2s.