how does this work?

Someone posted a solution to this thing a while ago, but I''m too lazy to look it up.

Here''s how it works: All the answers you will get when substracting the sum of the digits from any two-digit number will be a multiple of 9. Let''s say our first digit is b, a the second one is a. So we have...

10a + b - (a + b) = 10a + b - a - b = 9a

And, since a could be any integer between 1 and 9, your answer will be something like 9, 18, 27, and so on. The symbols are mixed every time, because you would notice how it works otherwise.

500x3

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

Notice that every one of those numbers have the same symbol.

If you think about it, after following the instructions, all possible solutions will have some thing in common.(multiples of 9 to be exact)

You will also notice that the symbols repeat next to certain numbers, though the symbols themselves change from refresh to refresh.

500x4

[edited by - wild_pointer on March 11, 2003 1:51:21 PM]

"Almost every time it guesses the correct symbol" - Well, if you do it right, it should actually be right EVERY time!

I hadn''t noticed the symbles changing, so sometimes I figured I would just stick with the same one, so didn''t bother to find it again.

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Exume my speling.