note
tachyon
<p>Hi, I don't know about in the US but in AUS we have 10 digit moblile numbers.
Given that each number has 3 possible letters you might use in round numbers
the search space is 59049 letter combinations per number
<p>Unfortunately the generation of the test keys is not *particularly* straight forward.
Using my ten digit scenario for each of the 59049 test cases we might have:
<p>one word (a) where a=10 letters
<p>two words (a,b) where a+b=10 letters,
<p>three words (a,b,c) where a+b+c = 10 letters
<p>.....
<p>ten words (a..j) where a+b+c+d+e+f+g+h+i+j=10 letters
If you remember the binomial expansion (as I vaguely do
- it was a while ago) you will remember the pyramid:
<code>
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
</code>
<p>What this shows us is that while there is obviously only one
test case for a ten letter match there are 9 possibilities
for an a+b=10 letter match, 36 possibilities for an a+b+c=10 letter match....
<p>Adding this up we find that there are 512 possibilities we need to consider
for each of the 59049 10 letter combinations. The total search space is 30,233,088.
I thought this might take a long time but that was when I thought it would be a
somewhat larger search space. Should be doable in under a minute of CPU time.
<p>more to follow...
<p>tachyon
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