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"The Flash Mind Reader" - How It Works

So my roommate sent me this Flash Mind Reading thing at
http://mr-31238.mr.valuehost.co.uk/assets/Flash/psychic.swf,
frustrated with it and herself, mystified about how the thing
worked. Lots of bloggers have linked to it, and it surprises me
the number of people who this frustrates. 

I figured it out.

Before I reveal how I figured it out, and why it works, let's
review the instructions:

"Choose any two digit number, add together both digits
 and then subtract the total from your original number.
 
 When you have the final number look it up on the chart
 and find the relevant symbol. Concentrate on the symbol
 and when you have it clearly in your mind click on the
 crystal ball and it will show you the symbol you are
 thinking of"



================================================================
STEP 1: Choose any two digit number
----------------------------------------------------------------
There are lots of those! Numbers 10 to 99. And to emphasize
all those choices we get a graphic filled with wingdings:
Dizzying! All those possibilities. All these numbers the computer
has to figure out when reading your mind! How can it do it?
Can it do it? Is it possible that a computer can read my mind?
================================================================


================================================================
STEP 2: add together both digits and then subtract the total
        from your original number.
----------------------------------------------------------------
Oh. Actually it's not going to read the number I thought of. It
wants me to do math first. It's still impressive if it can do it
though, because there are so many possibilities. If I think of
a really hard number that nobody will have thought of, I can
beat this stupid thing and prove it wrong!
================================================================


================================================================
STEP 3: When you have the final number look it up on the chart
 and find the relevant symbol. Concentrate on the symbol
 and when you have it clearly in your mind click on the
 crystal ball and it will show you the symbol you are
 thinking of
----------------------------------------------------------------
So you do the math, and the thing works! Aigh! and I chose my
number so carefully!
================================================================


================================================================
SO HOW DOES IT WORK?
----------------------------------------------------------------
It turns out that for all the possible numbers you can choose,
there are not all that many possible results to the calculation
you are asked to do on the number you choose.

Here's all of the possible numbers, alongside the calculations:
+---------------+-------------------+--------------------+
|    ALL TWO    |    THE DIGITS     |   THE DIGIT TOTAL  |
|     DIGIT     |      ADDED        |     SUBTRACTED     |
|    NUMBERS    |     TOGETHER      |   FROM THE NUMBER  |
+---------------+-------------------+--------------------+
|      10       |    1 + 0 =  1     |    10 -  1 =  9    |
|      11       |    1 + 1 =  2     |    11 -  2 =  9    |
|      12       |    1 + 2 =  3     |    12 -  3 =  9    |
|      13       |    1 + 3 =  4     |    13 -  4 =  9    |
|      14       |    1 + 4 =  5     |    14 -  5 =  9    |
|      15       |    1 + 5 =  6     |    15 -  6 =  9    |
|      16       |    1 + 6 =  7     |    16 -  7 =  9    |
|      17       |    1 + 7 =  8     |    17 -  8 =  9    |
|      18       |    1 + 8 =  9     |    18 -  9 =  9    |
|      19       |    1 + 9 = 10     |    19 - 10 =  9    |
|      20       |    2 + 0 =  2     |    20 -  2 = 18    |
|      21       |    2 + 1 =  3     |    21 -  3 = 18    |
|      22       |    2 + 2 =  4     |    22 -  4 = 18    |
|      23       |    2 + 3 =  5     |    23 -  5 = 18    |
|      24       |    2 + 4 =  6     |    24 -  6 = 18    |
|      25       |    2 + 5 =  7     |    25 -  7 = 18    |
|      26       |    2 + 6 =  8     |    26 -  8 = 18    |
|      27       |    2 + 7 =  9     |    27 -  9 = 18    |
|      28       |    2 + 8 = 10     |    28 - 10 = 18    |
|      29       |    2 + 9 = 11     |    29 - 11 = 18    |
|      30       |    3 + 0 =  3     |    30 -  3 = 27    |
|      31       |    3 + 1 =  4     |    31 -  4 = 27    |
|      32       |    3 + 2 =  5     |    32 -  5 = 27    |
|      33       |    3 + 3 =  6     |    33 -  6 = 27    |
|      34       |    3 + 4 =  7     |    34 -  7 = 27    |
|      35       |    3 + 5 =  8     |    35 -  8 = 27    |
|      36       |    3 + 6 =  9     |    36 -  9 = 27    |
|      37       |    3 + 7 = 10     |    37 - 10 = 27    |
|      38       |    3 + 8 = 11     |    38 - 11 = 27    |
|      39       |    3 + 9 = 12     |    39 - 12 = 27    |
|      40       |    4 + 0 =  4     |    40 -  4 = 36    |
|      41       |    4 + 1 =  5     |    41 -  5 = 36    |
|      42       |    4 + 2 =  6     |    42 -  6 = 36    |
|      43       |    4 + 3 =  7     |    43 -  7 = 36    |
|      44       |    4 + 4 =  8     |    44 -  8 = 36    |
|      45       |    4 + 5 =  9     |    45 -  9 = 36    |
|      46       |    4 + 6 = 10     |    46 - 10 = 36    |
|      47       |    4 + 7 = 11     |    47 - 11 = 36    |
|      48       |    4 + 8 = 12     |    48 - 12 = 36    |
|      49       |    4 + 9 = 13     |    49 - 13 = 36    |
|      50       |    5 + 0 =  5     |    50 -  5 = 45    |
|      51       |    5 + 1 =  6     |    51 -  6 = 45    |
|      52       |    5 + 2 =  7     |    52 -  7 = 45    |
|      53       |    5 + 3 =  8     |    53 -  8 = 45    |
|      54       |    5 + 4 =  9     |    54 -  9 = 45    |
|      55       |    5 + 5 = 10     |    55 - 10 = 45    |
|      56       |    5 + 6 = 11     |    56 - 11 = 45    |
|      57       |    5 + 7 = 12     |    57 - 12 = 45    |
|      58       |    5 + 8 = 13     |    58 - 13 = 45    |
|      59       |    5 + 9 = 14     |    59 - 14 = 45    |
|      60       |    6 + 0 =  6     |    60 -  6 = 54    |
|      61       |    6 + 1 =  7     |    61 -  7 = 54    |
|      62       |    6 + 2 =  8     |    62 -  8 = 54    |
|      63       |    6 + 3 =  9     |    63 -  9 = 54    |
|      64       |    6 + 4 = 10     |    64 - 10 = 54    |
|      65       |    6 + 5 = 11     |    65 - 11 = 54    |
|      66       |    6 + 6 = 12     |    66 - 12 = 54    |
|      67       |    6 + 7 = 13     |    67 - 13 = 54    |
|      68       |    6 + 8 = 14     |    68 - 14 = 54    |
|      69       |    6 + 9 = 15     |    69 - 15 = 54    |
|      70       |    7 + 0 =  7     |    70 -  7 = 63    |
|      71       |    7 + 1 =  8     |    71 -  8 = 63    |
|      72       |    7 + 2 =  9     |    72 -  9 = 63    |
|      73       |    7 + 3 = 10     |    73 - 10 = 63    |
|      74       |    7 + 4 = 11     |    74 - 11 = 63    |
|      75       |    7 + 5 = 12     |    75 - 12 = 63    |
|      76       |    7 + 6 = 13     |    76 - 13 = 63    |
|      77       |    7 + 7 = 14     |    77 - 14 = 63    |
|      78       |    7 + 8 = 15     |    78 - 15 = 63    |
|      79       |    7 + 9 = 16     |    79 - 16 = 63    |
|      80       |    8 + 0 =  8     |    80 -  8 = 72    |
|      81       |    8 + 1 =  9     |    81 -  9 = 72    |
|      82       |    8 + 2 = 10     |    82 - 10 = 72    |
|      83       |    8 + 3 = 11     |    83 - 11 = 72    |
|      84       |    8 + 4 = 12     |    84 - 12 = 72    |
|      85       |    8 + 5 = 13     |    85 - 13 = 72    |
|      86       |    8 + 6 = 14     |    86 - 14 = 72    |
|      87       |    8 + 7 = 15     |    87 - 15 = 72    |
|      88       |    8 + 8 = 16     |    88 - 16 = 72    |
|      89       |    8 + 9 = 17     |    89 - 17 = 72    |
|      90       |    9 + 0 =  9     |    90 -  9 = 81    |
|      91       |    9 + 1 = 10     |    91 - 10 = 81    |
|      92       |    9 + 2 = 11     |    92 - 11 = 81    |
|      93       |    9 + 3 = 12     |    93 - 12 = 81    |
|      94       |    9 + 4 = 13     |    94 - 13 = 81    |
|      95       |    9 + 5 = 14     |    95 - 14 = 81    |
|      96       |    9 + 6 = 15     |    96 - 15 = 81    |
|      97       |    9 + 7 = 16     |    97 - 16 = 81    |
|      98       |    9 + 8 = 17     |    98 - 17 = 81    |
|      99       |    9 + 9 = 18     |    99 - 18 = 81    |
+---------------+-------------------+--------------------+

We can now see that despite the fact that we get to choose from
numbers 10 to 99, really, there are only 9 possible numbers to
be put on our mind. So while there are lots of symbols provided,
we only have to worry about 9 of them: 9 18 27 36 45 54 63 72 81
And if we look close, we'll find that despite the fact that the
symbols are randomized, there is a peculiar consistency in the 
Mind Reader: multiples of 9 always share the same symbol.
Refresh the page and you'll see a new symbol, but 9 and 45 and
81 (and the rest of them) will always share that new symbol.
================================================================


================================================================
COMMENT: PSYCHIC THOUGHTS
----------------------------------------------------------------
It irritates me that people believe in psychic phenomena. We so
often attribute strange things to psychic powers. The truth is
that The Flash Mind Reader is a magic trick like all other magic
tricks. It uses misdirection (the many numbers, the randomized
symbols) and hocus pocus (the creepy fade-up of the symbol, the
accompanying sound, vaguely occult wingdings) to get us thinking
about psychic things. The magician only wants you to suspend
your disbelief to fool you. And that's how "The Flash Mind
Reader" works. Magic.

Magic in the sense of hacking with our perceptions and
assumptions. The truth is usually more mundane than we hope.
================================================================

                                       Joe Crawford 6 March 2003

================================================================

Addendum: reader Lee Fernandes writes that the piece could use
some clarification, and here's what he suggested:

Every outcome of the math results in a multiple of 9.  Every
multiple of 9 always shares the same symbol, so it is
inevitable that you and the Flash "Mind Reader" will always
pick the same symbol...you're both doing the same math.

================================================================

About Joe Crawford

Joe Crawford is a web designer and programmer. More information about his background, his employer, and his projects can be found at <http://artlung.com/> Read his current thoughts at artlung.com/blog.

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©2003 Joe Crawford.