Someone thinks of a number from 1 to 63. You show them six cards full of numbers, and they simply say yes or no: is your number on this card? After the sixth answer, you name their number. The cards are below, ready to copy, and the secret is a single glance at each card.
The cards
Copy these onto six index cards, or print this page. Each card’s first number (top left) is the key.
Card A
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
Card B
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
Card C
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
Card D
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
Card E
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
Card F
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
How to perform it
A secret number. “Think of any whole number from 1 to 63. Don’t tell me.”
Show the cards one at a time. For each card, ask: “Is your number on this card?” They answer yes or no.
Add the first numbers. For every card they say yes to, add up its first number (the top-left one). Card A starts with 1, B with 2, C with 4, D with 8, E with 16 and F with 32.
Name it. After the last card, the total is their number.
For example, if they say yes to cards A, C and E: 1 + 4 + 16 = 21. Their number is 21.
Why it works: every number from 1 to 63 can be made by adding some of 1, 2, 4, 8, 16 and 32 in exactly one way. That is binary counting. Each card lists every number that uses its starting value, so the cards they say yes to are exactly the pieces of their number.
Making it look like reading minds
Shuffle the cards first. The order does not matter, so mix them up and show them in a random order. It hides the fact that the first numbers double.
Add as you go. Keep a running total while they answer, so you can name the number the moment the last card goes down.
Ask them to concentrate. Stare at the card rather than at them. Kids, especially, will swear you were looking into their heads.
For younger children
Use only cards A to D and ask for a number from 1 to 15. Four questions is plenty of suspense for a seven-year-old.
Credit where due: An old puzzle built on binary numbers. We checked the cards below: every number from 1 to 63 appears on exactly the set of cards whose first numbers add up to it.