Guess My Number -- The Trick

Using the same numbers, I really could have told you to pick a number between 1 and 63, but that might have given it away for you computer science/math majors. All of the numbers between 1 and 63 (and thus those between 1 and 50) can be written with 6 binary digits (0s and 1s). You basically add together powers of 2 that have 1s in that position (binary is read from right to left). So, for example:


000001 = 1
000010 = 2
000011 = 1 + 2 = 3
000100 = 4
000101 = 1 + 4 = 5
000110 = 2 + 4 = 6
000111 = 1 + 2 + 4 = 7
001000 = 8
001001 = 1 + 8 = 9
001010 = 2 + 8 = 10
...
110110 = 2 + 4 + 16 + 32 = 54
110111 = 1 + 2 + 4 + 16 + 32 = 55
111000 = 8 + 16 + 32 = 56
111001 = 1 + 8 + 16 + 32 = 57
111010 = 2 + 8 + 16 + 32 = 58
111011 = 1 + 2 + 8 + 16 + 32 = 59
111100 = 4 + 8 + 16 + 32 = 60
111101 = 1 + 4 + 8 + 16 + 32 = 61
111110 = 2 + 4 + 8 + 16 + 32 = 62
111111 = 1 + 2 + 4 + 8 + 16 + 32 = 63

 


OK, so what does this have to do with anything? If you'll notice, each of the lists begins with a power of two. I mixed the order up a little, again, to throw you off. All the numbers in the list that starts with 1 have a 1 in the 1st (from the right) position when written in binary. If you checked the box for the list that starts with 1, I know that 1 will be an addend (one of the numbers I will add together to get your secret number). So basically when you check (or don't check) the little box for each list, you're telling me whether there is a 0 or a 1 in that power of 2's position and thus whether or not the first number in the list is an addend. For example, let's say your number was 27. You would fill out the form like this:

 
16 1 4 32 8 2
17 3 5 33 9 3
18 5 6 34 10 6
19 7 7 35 11 7
20 9 12 36 12 10
21 11 13 37 13 11
22 13 14 28 14 14
23 15 15 39 15 15
24 17 20 40 24 18
25 19 21 41 25 19
26 21 22 42 26 22
27 23 23 43 27 23
28 25 28 44 28 26
29 27 29 45 29 27
30 29 30 46 30 30
31 31 31 47 31 31
48 33 36 48 40 34
49 35 37 49 41 35
50 37 38 50 42 38
39 39 43 39
41 44 44 42
43 45 45 43
45 46 46 46
47 47 47 47
49 50
I know that your number is 27 because 16 + 1 + 8 + 2 = 27. ISN'T THAT NEAT!!!???!!!
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