CSE 111, Fall 04, BINARY MAGIC ANSWER

CSE 111, Fall 2004

BINARY MAGIC ANSWER

Here's how to do the trick:

Add up the number on the upper left corner of those cards that the audience answered "yes" to.

For example: An audience member who is 20 years old would pick out the third and fifth cards, which are the only ones with "20" on them. The numbers on the upper left corner of those cards are 4 and 16, respectively, which add up to 20!

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

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

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

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

And here's how it works:

The decimal numeral 20 is represented in 6-bit binary notation by:

010100

(Why 6-bits? Because that's how many "cards" there are in the trick. If you wanted to use 8-bit binary numerals, you would need 8 cards, and vice versa. That way, you could let the audience guess even larger numbers. Questions to think about: How many cards (or bits) would you need to allow the audience to choose any number from 0 to 100? And, if you used that many cards, what is the largest number the audience could choose?)

Using 0 to represent "no" and 1 to represent "yes", this numeral, 010100, can be interpreted to mean:

Now, letting "*" represent multiplication, we have:

(0 * 32)	+	(1 * 16)	+	(0 * 8)	+	(1 * 4)	+	(0 * 2)	+	(0 * 1)	=

0	+	16	+	0	+	4	+	0	+	0	=

		16	+			4					=

				20

Back to the trick