Why does it work?

To make this trick work you need to place the numbers from 1 to 63 in the lists in a particular arrangement. Notice that each of the numbers in the upper left corner of a list is a power of two.

32 = 2⁵, 16 = 2⁴, 8 = 2³, 4 = 2², 2 = 2¹ and 1 = 2⁰.

Start to create the lists by putting the powers of 2 in the upper left corners.

32

16

8

4

2

1

Each integer from 0 to 63 can be written in the form

a x 2⁵ + b x 2⁴ + c x 2³ + d x 2² + e x 2¹ + f x 2⁰ where a, b, c, d, e and f are either 0 or 1. This is often written abcdef₂ and called base two notation.

For each number between 1 and 63 first write it in base two notation. For example for 41.

41 = 1 x 32 + 0 x 16 + 0 x 8 + 1 x 4 + 0 x 2 + 1 x 1
= 1 x 2⁵ + 0 x 2⁴ + 1 x 2³ + 0 x 2² + 0 x 2¹ + 1 x 2⁰
= 101001₂

Place the number on each card that corresponds to a 1 in the base 2 representation. Thus, reading from left to right, 41 is placed on the first, third and sixth cards.

32	33	34	35
36	37	38	39
40	41	42	43
44	45	46	47
48	49	50	51
52	53	54	55
56	57	58	59
60	61	62	63

16	17	18	19
20	21	22	23
24	25	26	27
28	29	30	31
48	49	50	51
52	53	54	55
56	57	58	59
60	61	62	63

8	9	10	11
12	13	14	15
24	25	26	27
28	29	30	31
40	41	42	43
44	45	46	47
56	57	58	59
60	61	62	63

4	5	6	7
12	13	14	15
20	21	22	23
28	29	30	31
36	37	38	39
44	45	46	47
52	53	54	55
60	61	62	63

2	3	6	7
10	11	14	15
18	19	22	23
26	27	30	31
34	35	38	39
42	43	46	47
50	51	54	55
58	59	62	63

1	3	5	7
9	11	13	15
17	19	21	23
25	27	29	31
33	35	37	39
41	43	45	47
49	51	53	55
57	59	61	63

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