YOUR LUCKY (MAGIC) SQUARE:
This is an interesting performance you can
do with some people. You start off
explaining that you will calculate their “Lucky Square”, but you need their
help. You will pick a number to start
with, but after that they will pick the numbers, and decide whether or not to
add or subtract.
Amazingly, their lucky square turns out to
be a magic square (all the rows, all of the columns, and both diagonals sum to
the same lucky number). You explain that
the square that they helped you create has some “strong magic” and they should
carry it with them always.
After doing this trick a few times you will
have the order that you will calculate their numbers memorized. But for now you need to memorize the chart
below:
8

1

7

This is the position
grid you will use. You will write the
first number in position 1, the second number in position two, the third
number in position 3, etc. When I
refer to using the number in position 1, it means the top middle
position. If I refer to using a number
in position 2 it means the bottom left position. Position 3 means the middle of the right
column.

5

6

3


2

9

4





First obtain the participant’s birthday,
and write it down above your blank grid.
It does not matter if you write it down with month first, or day first
(MM/DD/YY or DD/MM/YY). You may choose
to use a four digit year instead of a two digit year, and this may be more
helpful to you if the two digit year is a small number (it will avoid having
negative number is the square). If they
don’t want to tell you their birthday ask them what three numbers seem to be
the luckiest for them, and to start the trick start with the largest.
Suppose their birthday is:
“3 – 14 – 81”

81


If
the year offers only a small number, such as the year 2003, go ahead and
write down all four digits to avoid doing a subtraction that will lead to
negative number. If you are not sure,
go ahead and write down the four digit year – it won’t hurt. In this case, it I add or subtract it
probably won’ be an issue. Now go ahead
and write the year number in position 1.
Tell your participant: “This is one of the most important numbers for
your square.”













81


Now ask the participant
which number they want to use next (either the 3 or the 14), and ask if they
want to add or subtract the chosen number.
Suppose they chose the 14, and want to subtract. Then take the 81 and subtract 14 (which is
67), and then subtract 14 again (which is 53). Write the 67 in position 2, and write the
53 in position 3. And tell the
participant that “These are the three most important numbers in your Lucky
Magic Square.”



53


67








81

73

Next, ask the
participant what number they want to use next, and do they want to add or
subtract. Suppose they choose this
time to use the three, and they want to add it. Start with the 81 in position 1, then add
81 + 3 = 84, and then add it again. 84
+ 3 = 87. Write the 84 in position 4,
and the 87 in position 5. Next use the
67 in position 2, add 67 + 3 = 70, then add 70 + 3 = 73. Write the 70 in position 6, and the 73 in
position 7.

87

70

53


67


84





56

81

73

Finally, we use the 53
in position 3, and add 53 + 3 (which is 56) and add 56 + 3 (which is 59). Write the 56 in position 8, and the 59 in
position 9.
This completes the magic
square, but you now have to explain why this square is so special, or so
lucky. “You are not going to believe
this …” Show them that each row has
the same sum (in this case 210), and that each column has the same sum (in
this case it is still 210), and that each main diagonal has the same sum (in
this case 210 again).

87

70

53


67

59

84





Explain that not all Lucky Squares have
this particular property (even though they do).
It is very magical and is therefore very lucky. They need to make sure that they carry it
with them at all times, and make sure they don’t lose it. Give them a paper copy of their Lucky Square.
Now suppose that the next birthday you are
asked to use is:
“8 – 23 – 14”
Please be very carefully preforming and
explaining what you are doing at each step – because the participant is either very
young or very old.

2014


In this case it will be
better to use a four digit year. So
write 2014 in position 1.
Then we ask which number
the participant wants to use next, and if they wish to add or subtract the
number. Suppose they say they want to
add using the 8. In position 2 we add
2014 + 8 (which is 2022), and in position 3 we add 8 again (which is 2030). Don’t forget to explain that these are the three
most important numbers in their lucky square.



2033


2022








2014


Now we ask again which
number do they want to use next, and do they want to add or subtract.
Suppose they want to use
the 23 next, and they want to add again.
Starting with 2014 in position 1, we add 23 (which is 2037) and write
the answer in position 4, and then add 23 again (which is 2050) and write the
answer in position 5.

2050


2030


2022


2037





2053

2014

2068

Remember, we are still adding 23.
We take the number in position 2 and add
23 twice (which is 2045 and 2068) and write them in positions 5 and 6.
Finally, we take the number in position 3
and add 23 twice (which is 2053 and 2076) and write these numbers in
positions 8 and 9.
The square is completed,
and it has a magic constant of 6135.
Every row, every column, and both main diagonals sum to
Tell them, “You are not
going to believe this but ...” and show them the magical properties of their
square.

2050

2045

2030


2022

2076

2037





Again, don’t forget to explain that they
have a very special lucky square, you could even say magical since most other
lucky squares don’t have this property.
Make sure you give them a written copy of their lucky square, and
explain they should carry it with them always.
The material above was adapted from: “Mathematical
Magic” by William Simon
Sources
“Mathematical Magic” by William Simon
David
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