January 9, 2000

Birthday Magic Square

Robertson/Shaxon/Vincent

I was immediately taken with Allan Shaxon's "Birthday Magic Square" in Jan. 2000 British Ring Parade in Linking Ring. He credits the unusual magic square to Leslie Vincent. It's a 3 X 3 magic square constructed using nothing but the month, day and year of a person's birthday.

Ask someone to name their birth-date (or some other date of significance to them). Let's say they named December 28, 1963. Write it on a piece of paper like this: 12/28/63

Draw a 3 X 3 square below the birth-date, then fill it in using nothing but combinations of the month, day and year of the birth date. When you've filled in the magic square, show that all the rows, columns, and the two diagonals all add up to the same number, in this case: 309. First impact! Then, drawing on numerology, you add up the digits (3 + 0 + 9) to get 12, then add them up again (1+ 2) until you have a single digit: 3. That is their lucky birthday number.

On the left below is birthday magic square filled in for 12/28/63. Next to it is a square with the numbers from 1 to 9 in the cells, representing the order you fill in the cells.

 115 63 131 2 5 3 119 103 87 9 1 7 75 143 91 6 4 8

Assuming M/D/Y are Month/Day/Year:

1 = M + D + Y (12 + 28 + 63 = 103). Let's call this "A" hereafter.

2 = "A" + M (103 + 12 = 115)

3 = "A" + D (103 + 28 = 131)

4 = "A" + M + D (103 + 12 + 28 = 143)

5 = Y (63)

6 = Y + M (63 + 12 = 75).

7 = Last Figure + M (75 + 12 = 87)

8 = Y + D (63 + 28 = 91).

9 = Last Figure + D (91 + 28 = 119)

This forms a magic square. This works because the construction method forces each row, column, and diagonal to add up to 3M + 3D + 3. Here's what the squares are really filled with. See yourself that all rows, columns and diagonals add up to 3M + 3D + 3Y.

 2M+D+Y Y M+2D+Y Y+2D M+D+Y Y+2M Y+M 2M+2D+Y Y+D

Note: other than adapting this from the European order of D/M/Y, to the normal U.S. order of M/D/Y, this is exactly as in Shaxon's original effect.

Now this is nice in itself and should serve as a great impromptu item when you've got absolutely nothing but pencil and paper. But we can add a little more magic (& puffery) to it.

First, as soon as you see the birthday you can arrive at the magic number. Just add up the digits and cast off 9's until you arrive at a single digit, then multiply it by 3 and cast off 9's. Here's what you get. The first row is the single digit and the 2nd what you get after to multiply by 3 and cast off 9's:

1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9

3 - 6 - 9 - 3 - 6 - 9 - 3 - 6 - 9

You can see the simple pattern that forms so that you instantly know what the magic number is: either 3, 6, 0r 9. Just cast off 9's until you get a single number. If it's bigger than 3, cast off 3's, so you arrive at either 1, 2, or 3. Multiply that one by 3. It's not as hard as this all sounds:
just look at the above line.

Ok, so you know the number instantly. You can immediately jot it on a piece of paper and hand to the spectator, then proceed with the magic square. At the end you can show that you predicted the magic number in advance. I made up some small preprinted papers ready to be filled with the birthday, magic square and magic number. If you decide to do the same, simply calculate the magic number as soon as you write in the birth-date, then jot on the back of the paper "your magic number is (whatever)" as your prediction.

Since there are only 3 possibilities, however, you could have a 3 on top of the deck and a 6 on the bottom. Before you ever ask for the birthdate, have the deck cut and do the crossing the cut force. At the end, if their magic number is 3, show the card cut at (on top) is a 3. If a 6, show that the spectator cut to a 6 (underneath). If a 9, the spectator cut to a 3 and a 6 which add up to 9.

Audiences are always fascinated by magic squares and a spectator is likely to treasure one constructed using their birth-date.