Psychic Ball

Flash Mind Reader Demystified

based on The Flash Mind Reader by Andy Naughton

Let us take a look into the crystal ball that is math ...

First, the question. It instructs you to pick any two-digit number (that is, any number between 10 and 99), add the two digits together, and then subtract that amount from the original number. 

Andy gives this example:

If you chose 23, then 2+3 = 5 and 23 minus 5 will give you your answer.

This page (the one you're reading now) magically performed all the possible choices (from 10 to 99) to the right, magically producing all the correct answers!

For emphasis, every unique number is a different color. You'll quickly notice the first trick here; Your final answer only changes every ten numbers!

Subtracting just the second digit instead of the sum of the digits, in his example the 3, simply turns the one's digit into a 0. To illustrate this, lets try the trick with that change (changing his example to If you chose 23, then 23 minus 3 will give you your answer.):

20 - 0 = 20
21 - 1 = 20
22 - 2 = 20
23 - 3 = 20
24 - 4 = 20
25 - 5 = 20

So the possible answers with doing just half the work are:

10 20 30 40 50 60 70 80 90

These aren't our answers though because we've only done half the work.

So now let's subtract the first digit from each of these (and since the tens digit only changes every ten numbers, we only need to do it on these numbers). In doing so, we end up with:

09 18 27 36 45 54 63 72 81

As luck would have it, these are the numbers you see on the right column!

So lets look at the answer key. I've highlighted our answers from above:

Answer Chart

Lo and behold, all of our answers are the same symbol! This means that no matter which one you picked, your symbol is the smiley face.

So pick one. Are we right? Of course! 
Clicking the ball reveals:

Psychic Ball

This animation is tricky though! Once you click the ball the answer key disappears so you can't easily see what other answers have the same symbol.

That's not all though, when you try again, Andy randomly changes the symbols! Rest assured though; every time you play it our correct answers will always be the same symbol, and correct no less. 

I've heard some people say that they tried and got it wrong. There are two possible reasons for it. 

The first and most likely reason is human error; you goofed! Either you did the math wrong or you remembered the wrong symbol.

The second and rarest (and perhaps not even possible!) reason is trickery; he may occasionally make it error. If any one of the numbers I listed wasn't the correct symbol, then this is the case.

The proof of this? Call the two digit number xy and you can simplify as such:

(10x + y) - (x + y) = 9x

So any multiple of 9 will be correct here.


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