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That's quite an amazing approximation. Even at values of 100000, it's only ~0.0007 off.
Try to graph
If you can fit that curve to a known and non-log function, you've got an exact approximation.
However, I believe:
Which would just mean that the curve of the difference goes off to infinity. So I'm thinking either a polynomial or exponential.
What's "leet" got to do with this?
Leet as in leet speak, as in slang on the internet, f00.
He was blind and crossing a street.
Just to clarify:
Now we have:
This isn't exactly clear, so let's write it in a different way:
Or:
Or even:
Is that clearer?
O my.. i let my program running all night long but it crashed at size 43!!!!!! :\\\
Crashed? What language did you program it in?
I should have size 62 by the next time I post.
(a / b) / (c / d) = (a / b) * (d / c)
(3 / 2) / (4 / 5) = (3 / 2) * (5 / 4) = 15 / 8
Be careful writing 1/4x. It looks like (1/4)x, when in reality it's 1 / (4x).
y = 4 + 1/4x = 4 + 4^-1 * x^-1, that 4 is on the bottom as well. Of course, 4^-1 = 1/4
y = 4 + 1/4 * x^-1
Try doing that.
The reason why I did that is because x and x*, and z and z*, have a lot of the same terms in them, which you can take advantage of if you put them in full complex form.
From there, it's just plugging them in and trying to solve for c and d.
First, start by doing a few quick substitutions:
x = a + bi (where a and b are real)
x* = a - bi
z = c + di (where c and d are real)
z* = c - di
xx* = (a + bi)(a - bi) = a^2 + b^2
z - z* = c + di - (c - di) = 2di
So:
a^2 + b^2 + 3(2di) = 13 + 12i
Since i is the only possible imaginary value (all other variables must be real):
a^2 + b^2 = 13 and 6di = 12i
di = 2i, and since d must be real, d = 2
So z = c + 2i, where c is any real number. The simpilest solution is z = 2i (c = 0)
Mr. Theft just likes to buy a lot of shoes from that one store.
Please give the other two clues.
Here are the solutions from size 32 to 35, they seem to increase as the size does. Also note that each solution appears twice, once forward and once in the reverse order.
Size: 32
1 8 28 21 4 32 17 19 30 6 3 13 12 24 25 11 5 31 18 7 29 20 16 9 27 22 14 2 23 26 10 15
Size: 32
1 15 10 26 23 2 14 22 27 9 16 20 29 7 18 31 5 11 25 24 12 13 3 6 30 19 17 32 4 21 28 8
Size: 33
1 8 28 21 4 32 17 19 30 6 3 13 12 24 25 11 5 20 29 7 18 31 33 16 9 27 22 14 2 23 26 10 15
Size: 33
1 15 10 26 23 2 14 22 27 9 16 33 31 18 7 29 20 5 11 25 24 12 13 3 6 30 19 17 32 4 21 28 8
Size: 34
1 3 13 12 4 32 17 8 28 21 15 34 30 19 6 10 26 23 2 14 22 27 9 16 33 31 18 7 29 20 5 11 25 24
Size: 34
1 3 13 12 24 25 11 5 20 29 7 18 31 33 16 9 27 22 14 2 23 26 10 15 34 30 6 19 17 32 4 21 28 8
Size: 34
1 3 13 12 24 25 11 14 22 27 9 16 33 31 18 7 29 20 5 4 32 17 19 6 30 34 2 23 26 10 15 21 28 8
Size: 34
1 3 13 12 24 25 11 14 22 27 9 16 33 31 18 7 29 20 5 4 32 17 19 30 6 10 26 23 2 34 15 21 28 8
Size: 34
1 3 13 23 26 10 6 19 30 34 2 14 22 27 9 16 33 31 18 7 29 20 5 11 25 24 12 4 32 17 8 28 21 15
Size: 34
1 3 13 23 26 10 6 30 19 17 32 4 12 24 25 11 5 20 29 7 18 31 33 16 9 27 22 14 2 34 15 21 28 8
Size: 34
1 3 22 27 9 16 33 31 18 7 29 20 5 4 32 17 19 6 30 34 2 14 11 25 24 12 13 23 26 10 15 21 28 8
Size: 34
1 3 22 27 9 16 33 31 18 7 29 20 5 4 32 17 19 30 6 10 26 23 13 12 24 25 11 14 2 34 15 21 28 8
Size: 34
1 3 33 31 18 7 29 20 16 9 27 22 14 2 34 30 6 19 17 32 4 5 11 25 24 12 13 23 26 10 15 21 28 8
Size: 34
1 3 33 31 18 7 29 20 16 9 27 22 14 2 34 30 19 6 10 26 23 13 12 24 25 11 5 4 32 17 8 28 21 15
Size: 34
1 8 28 21 4 32 17 19 6 30 34 15 10 26 23 2 14 22 27 9 16 33 31 18 7 29 20 5 11 25 24 12 13 3
Size: 34
1 8 28 21 15 10 26 23 2 34 30 6 19 17 32 4 5 20 29 7 18 31 33 16 9 27 22 14 11 25 24 12 13 3
Size: 34
1 8 28 21 15 10 26 23 13 12 24 25 11 5 4 32 17 19 6 30 34 2 14 22 27 9 16 20 29 7 18 31 33 3
Size: 34
1 8 28 21 15 10 26 23 13 12 24 25 11 14 2 34 30 6 19 17 32 4 5 20 29 7 18 31 33 16 9 27 22 3
Size: 34
1 8 28 21 15 34 2 14 11 25 24 12 13 23 26 10 6 30 19 17 32 4 5 20 29 7 18 31 33 16 9 27 22 3
Size: 34
1 8 28 21 15 34 2 14 22 27 9 16 33 31 18 7 29 20 5 11 25 24 12 4 32 17 19 30 6 10 26 23 13 3
Size: 34
1 8 28 21 15 34 2 23 26 10 6 30 19 17 32 4 5 20 29 7 18 31 33 16 9 27 22 14 11 25 24 12 13 3
Size: 34
1 8 28 21 15 34 30 19 17 32 4 12 13 3 6 10 26 23 2 14 22 27 9 16 33 31 18 7 29 20 5 11 25 24
Size: 34
1 15 21 28 8 17 32 4 5 11 25 24 12 13 23 26 10 6 19 30 34 2 14 22 27 9 16 20 29 7 18 31 33 3
Size: 34
1 15 21 28 8 17 32 4 12 24 25 11 5 20 29 7 18 31 33 16 9 27 22 14 2 34 30 19 6 10 26 23 13 3
Size: 34
1 24 25 11 5 20 29 7 18 31 33 16 9 27 22 14 2 23 26 10 6 3 13 12 4 32 17 19 30 34 15 21 28 8
Size: 34
1 24 25 11 5 20 29 7 18 31 33 16 9 27 22 14 2 23 26 10 6 19 30 34 15 21 28 8 17 32 4 12 13 3
Size: 35
1 3 6 19 30 34 2 7 18 31 33 16 9 27 22 14 11 25 24 12 13 23 26 10 15 21 28 8 17 32 4 5 20 29 35
Size: 35
1 3 13 12 4 32 17 8 28 21 15 34 30 19 6 10 26 23 2 7 18 31 33 16 9 27 22 14 35 29 20 5 11 25 24
Size: 35
1 3 13 12 24 25 11 5 4 32 17 8 28 21 15 34 30 19 6 10 26 23 2 14 22 27 9 7 18 31 33 16 20 29 35
Size: 35
1 3 13 12 24 25 11 5 20 29 35 14 22 27 9 16 33 31 18 7 2 23 26 10 15 34 30 6 19 17 32 4 21 28 8
Size: 35
1 3 13 12 24 25 11 14 22 27 9 16 33 31 18 7 2 23 26 10 6 19 30 34 15 21 28 8 17 32 4 5 20 29 35
Size: 35
1 3 13 23 26 10 6 19 30 34 2 7 18 31 33 16 9 27 22 14 35 29 20 5 11 25 24 12 4 32 17 8 28 21 15
Size: 35
1 3 13 23 26 10 6 30 19 17 32 4 12 24 25 11 5 20 29 35 14 22 27 9 16 33 31 18 7 2 34 15 21 28 8
Size: 35
1 3 22 27 9 7 18 31 33 16 20 29 35 14 2 34 30 6 19 17 32 4 5 11 25 24 12 13 23 26 10 15 21 28 8
Size: 35
1 3 22 27 9 7 18 31 33 16 20 29 35 14 2 34 30 19 6 10 26 23 13 12 24 25 11 5 4 32 17 8 28 21 15
Size: 35
1 3 22 27 9 16 33 31 18 7 2 14 11 25 24 12 13 23 26 10 6 19 30 34 15 21 28 8 17 32 4 5 20 29 35
Size: 35
1 3 22 27 9 16 33 31 18 7 2 14 35 29 20 5 11 25 24 12 13 23 26 10 15 34 30 6 19 17 32 4 21 28 8
Size: 35
1 3 22 27 9 16 33 31 18 7 2 34 30 6 19 17 32 4 5 20 29 35 14 11 25 24 12 13 23 26 10 15 21 28 8
Size: 35
1 3 22 27 9 16 33 31 18 7 2 34 30 19 6 10 26 23 13 12 24 25 11 14 35 29 20 5 4 32 17 8 28 21 15
Size: 35
1 8 28 21 4 32 17 19 6 30 34 2 14 35 29 7 18 31 33 3 22 27 9 16 20 5 11 25 24 12 13 23 26 10 15
Size: 35
1 8 28 21 4 32 17 19 6 30 34 2 14 35 29 20 16 33 3 22 27 9 7 18 31 5 11 25 24 12 13 23 26 10 15
Size: 35
1 8 28 21 4 32 17 19 6 30 34 15 10 26 23 2 7 18 31 33 16 9 27 22 14 35 29 20 5 11 25 24 12 13 3
Size: 35
1 8 28 21 4 32 17 19 6 30 34 15 10 26 23 2 14 22 27 9 7 18 31 5 11 25 24 12 13 3 33 16 20 29 35
Size: 35
1 8 28 21 4 32 17 19 6 30 34 15 10 26 23 2 14 22 27 9 16 20 5 11 25 24 12 13 3 33 31 18 7 29 35
Size: 35
1 8 28 21 4 32 17 19 6 30 34 15 10 26 23 13 12 24 25 11 5 20 29 35 14 2 7 18 31 33 16 9 27 22 3
Size: 35
1 8 28 21 4 32 17 19 30 6 3 22 27 9 16 33 31 18 7 29 20 5 11 25 24 12 13 23 26 10 15 34 2 14 35
Size: 35
1 8 28 21 4 32 17 19 30 6 3 33 16 9 27 22 14 11 25 24 12 13 23 26 10 15 34 2 7 18 31 5 20 29 35
Size: 35
1 8 28 21 4 32 17 19 30 6 10 26 23 13 12 24 25 11 5 20 16 9 27 22 3 33 31 18 7 29 35 14 2 34 15
Size: 35
1 8 28 21 4 32 17 19 30 6 10 26 23 13 12 24 25 11 5 31 18 7 9 27 22 3 33 16 20 29 35 14 2 34 15
Size: 35
1 8 28 21 15 10 26 23 2 34 30 6 19 17 32 4 5 11 25 24 12 13 3 33 31 18 7 29 20 16 9 27 22 14 35
Size: 35
1 8 28 21 15 10 26 23 2 34 30 6 19 17 32 4 5 20 16 9 27 22 14 11 25 24 12 13 3 33 31 18 7 29 35
Size: 35
1 8 28 21 15 10 26 23 2 34 30 6 19 17 32 4 5 20 29 7 18 31 33 16 9 27 22 3 13 12 24 25 11 14 35
Size: 35
1 8 28 21 15 10 26 23 2 34 30 6 19 17 32 4 5 31 18 7 9 27 22 14 11 25 24 12 13 3 33 16 20 29 35
Size: 35
1 8 28 21 15 10 26 23 2 34 30 6 19 17 32 4 12 13 3 33 16 20 29 35 14 22 27 9 7 18 31 5 11 25 24
Size: 35
1 8 28 21 15 10 26 23 2 34 30 6 19 17 32 4 12 13 3 33 31 18 7 29 35 14 22 27 9 16 20 5 11 25 24
Size: 35
1 8 28 21 15 10 26 23 13 3 22 27 9 16 33 31 18 7 29 20 5 11 25 24 12 4 32 17 19 6 30 34 2 14 35
Size: 35
1 8 28 21 15 10 26 23 13 3 33 16 9 27 22 14 11 25 24 12 4 32 17 19 6 30 34 2 7 18 31 5 20 29 35
Size: 35
1 8 28 21 15 10 26 23 13 12 4 32 17 19 6 30 34 2 14 35 29 7 18 31 33 3 22 27 9 16 20 5 11 25 24
Size: 35
1 8 28 21 15 10 26 23 13 12 4 32 17 19 6 30 34 2 14 35 29 20 16 33 3 22 27 9 7 18 31 5 11 25 24
Size: 35
1 8 28 21 15 10 26 23 13 12 24 25 11 5 4 32 17 19 6 30 34 2 14 35 29 20 16 33 31 18 7 9 27 22 3
Size: 35
1 8 28 21 15 10 26 23 13 12 24 25 11 14 2 34 30 6 19 17 32 4 5 20 16 9 27 22 3 33 31 18 7 29 35
Size: 35
1 8 28 21 15 10 26 23 13 12 24 25 11 14 2 34 30 6 19 17 32 4 5 31 18 7 9 27 22 3 33 16 20 29 35
Size: 35
1 8 28 21 15 10 26 23 13 12 24 25 11 14 35 29 20 5 4 32 17 19 6 30 34 2 7 18 31 33 16 9 27 22 3
Size: 35
1 8 28 21 15 34 2 7 18 31 33 16 9 27 22 14 35 29 20 5 11 25 24 12 4 32 17 19 30 6 10 26 23 13 3
Size: 35
1 8 28 21 15 34 2 14 11 25 24 12 13 23 26 10 6 30 19 17 32 4 5 20 16 9 27 22 3 33 31 18 7 29 35
Size: 35
1 8 28 21 15 34 2 14 11 25 24 12 13 23 26 10 6 30 19 17 32 4 5 31 18 7 9 27 22 3 33 16 20 29 35
Size: 35
1 8 28 21 15 34 2 14 22 27 9 7 18 31 5 11 25 24 12 4 32 17 19 30 6 10 26 23 13 3 33 16 20 29 35
Size: 35
1 8 28 21 15 34 2 14 22 27 9 16 20 5 11 25 24 12 4 32 17 19 30 6 10 26 23 13 3 33 31 18 7 29 35
Size: 35
1 8 28 21 15 34 2 23 26 10 6 30 19 17 32 4 5 11 25 24 12 13 3 33 31 18 7 29 20 16 9 27 22 14 35
Size: 35
1 8 28 21 15 34 2 23 26 10 6 30 19 17 32 4 5 20 16 9 27 22 14 11 25 24 12 13 3 33 31 18 7 29 35
Size: 35
1 8 28 21 15 34 2 23 26 10 6 30 19 17 32 4 5 20 29 7 18 31 33 16 9 27 22 3 13 12 24 25 11 14 35
Size: 35
1 8 28 21 15 34 2 23 26 10 6 30 19 17 32 4 5 31 18 7 9 27 22 14 11 25 24 12 13 3 33 16 20 29 35
Size: 35
1 8 28 21 15 34 2 23 26 10 6 30 19 17 32 4 12 13 3 33 16 20 29 35 14 22 27 9 7 18 31 5 11 25 24
Size: 35
1 8 28 21 15 34 2 23 26 10 6 30 19 17 32 4 12 13 3 33 31 18 7 29 35 14 22 27 9 16 20 5 11 25 24
Size: 35
1 8 28 21 15 34 30 19 17 32 4 5 11 25 24 12 13 3 6 10 26 23 2 14 22 27 9 7 18 31 33 16 20 29 35
Size: 35
1 8 28 21 15 34 30 19 17 32 4 5 11 25 24 12 13 23 26 10 6 3 33 31 18 7 2 14 22 27 9 16 20 29 35
Size: 35
1 8 28 21 15 34 30 19 17 32 4 12 13 3 6 10 26 23 2 7 18 31 33 16 9 27 22 14 35 29 20 5 11 25 24
Size: 35
1 8 28 21 15 34 30 19 17 32 4 12 13 23 26 10 6 3 22 27 9 16 33 31 18 7 2 14 35 29 20 5 11 25 24
Size: 35
1 15 10 26 23 13 12 24 25 11 5 20 16 9 27 22 3 33 31 18 7 29 35 14 2 34 30 6 19 17 32 4 21 28 8
Size: 35
1 15 10 26 23 13 12 24 25 11 5 31 18 7 9 27 22 3 33 16 20 29 35 14 2 34 30 6 19 17 32 4 21 28 8
Size: 35
1 15 21 28 8 17 32 4 5 11 25 24 12 13 23 26 10 6 19 30 34 2 14 35 29 20 16 33 31 18 7 9 27 22 3
Size: 35
1 15 21 28 8 17 32 4 5 20 29 35 14 11 25 24 12 13 23 26 10 6 19 30 34 2 7 18 31 33 16 9 27 22 3
Size: 35
1 15 21 28 8 17 32 4 12 13 23 26 10 6 19 30 34 2 14 35 29 7 18 31 33 3 22 27 9 16 20 5 11 25 24
Size: 35
1 15 21 28 8 17 32 4 12 13 23 26 10 6 19 30 34 2 14 35 29 20 16 33 3 22 27 9 7 18 31 5 11 25 24
Size: 35
1 15 21 28 8 17 32 4 12 24 25 11 5 20 16 9 27 22 14 2 34 30 19 6 10 26 23 13 3 33 31 18 7 29 35
Size: 35
1 15 21 28 8 17 32 4 12 24 25 11 5 20 29 7 18 31 33 16 9 27 22 3 13 23 26 10 6 19 30 34 2 14 35
Size: 35
1 15 21 28 8 17 32 4 12 24 25 11 5 20 29 35 14 22 27 9 16 33 31 18 7 2 34 30 19 6 10 26 23 13 3
Size: 35
1 15 21 28 8 17 32 4 12 24 25 11 5 31 18 7 9 27 22 14 2 34 30 19 6 10 26 23 13 3 33 16 20 29 35
Size: 35
1 15 21 28 8 17 32 4 12 24 25 11 14 22 27 9 16 33 3 13 23 26 10 6 19 30 34 2 7 18 31 5 20 29 35
Size: 35
1 15 34 2 14 35 29 7 18 31 33 3 22 27 9 16 20 5 11 25 24 12 13 23 26 10 6 30 19 17 32 4 21 28 8
Size: 35
1 15 34 2 14 35 29 20 16 33 3 22 27 9 7 18 31 5 11 25 24 12 13 23 26 10 6 30 19 17 32 4 21 28 8
Size: 35
1 24 25 11 5 20 16 9 27 22 3 33 31 18 7 29 35 14 2 34 30 6 19 17 32 4 12 13 23 26 10 15 21 28 8
Size: 35
1 24 25 11 5 20 16 9 27 22 3 33 31 18 7 29 35 14 2 34 30 19 6 10 26 23 13 12 4 32 17 8 28 21 15
Size: 35
1 24 25 11 5 20 16 9 27 22 14 2 23 26 10 6 19 30 34 15 21 28 8 17 32 4 12 13 3 33 31 18 7 29 35
Size: 35
1 24 25 11 5 20 16 9 27 22 14 35 29 7 18 31 33 3 13 12 4 32 17 19 6 30 34 2 23 26 10 15 21 28 8
Size: 35
1 24 25 11 5 20 16 9 27 22 14 35 29 7 18 31 33 3 13 12 4 32 17 19 30 6 10 26 23 2 34 15 21 28 8
Size: 35
1 24 25 11 5 20 29 7 18 31 33 16 9 27 22 3 13 12 4 32 17 8 28 21 15 34 30 19 6 10 26 23 2 14 35
Size: 35
1 24 25 11 5 20 29 35 14 2 7 18 31 33 16 9 27 22 3 6 10 26 23 13 12 4 32 17 19 30 34 15 21 28 8
Size: 35
1 24 25 11 5 20 29 35 14 22 27 9 16 33 31 18 7 2 23 26 10 6 3 13 12 4 32 17 19 30 34 15 21 28 8
Size: 35
1 24 25 11 5 20 29 35 14 22 27 9 16 33 31 18 7 2 23 26 10 6 19 30 34 15 21 28 8 17 32 4 12 13 3
Size: 35
1 24 25 11 5 31 18 7 9 27 22 3 33 16 20 29 35 14 2 34 30 6 19 17 32 4 12 13 23 26 10 15 21 28 8
Size: 35
1 24 25 11 5 31 18 7 9 27 22 3 33 16 20 29 35 14 2 34 30 19 6 10 26 23 13 12 4 32 17 8 28 21 15
Size: 35
1 24 25 11 5 31 18 7 9 27 22 14 2 23 26 10 6 19 30 34 15 21 28 8 17 32 4 12 13 3 33 16 20 29 35
Size: 35
1 24 25 11 5 31 18 7 9 27 22 14 35 29 20 16 33 3 13 12 4 32 17 19 6 30 34 2 23 26 10 15 21 28 8
Size: 35
1 24 25 11 5 31 18 7 9 27 22 14 35 29 20 16 33 3 13 12 4 32 17 19 30 6 10 26 23 2 34 15 21 28 8
Size: 35
1 24 25 11 14 22 27 9 16 33 3 13 12 4 32 17 8 28 21 15 34 30 19 6 10 26 23 2 7 18 31 5 20 29 35
Size: 35
1 35 14 2 23 26 10 6 19 30 34 15 21 28 8 17 32 4 12 13 3 22 27 9 16 33 31 18 7 29 20 5 11 25 24
Size: 35
1 35 14 2 34 15 10 26 23 13 12 24 25 11 5 20 29 7 18 31 33 16 9 27 22 3 6 30 19 17 32 4 21 28 8
Size: 35
1 35 14 2 34 30 6 19 17 32 4 12 24 25 11 5 20 29 7 18 31 33 16 9 27 22 3 13 23 26 10 15 21 28 8
Size: 35
1 35 14 2 34 30 19 6 10 26 23 13 3 22 27 9 16 33 31 18 7 29 20 5 11 25 24 12 4 32 17 8 28 21 15
Size: 35
1 35 14 11 25 24 12 13 3 22 27 9 16 33 31 18 7 29 20 5 4 32 17 19 6 30 34 2 23 26 10 15 21 28 8
Size: 35
1 35 14 11 25 24 12 13 3 22 27 9 16 33 31 18 7 29 20 5 4 32 17 19 30 6 10 26 23 2 34 15 21 28 8
Size: 35
1 35 14 22 27 9 16 20 29 7 18 31 33 3 13 12 24 25 11 5 4 32 17 19 6 30 34 2 23 26 10 15 21 28 8
Size: 35
1 35 14 22 27 9 16 20 29 7 18 31 33 3 13 12 24 25 11 5 4 32 17 19 30 6 10 26 23 2 34 15 21 28 8
Size: 35
1 35 29 7 18 31 33 3 13 12 4 32 17 8 28 21 15 34 30 19 6 10 26 23 2 14 22 27 9 16 20 5 11 25 24
Size: 35
1 35 29 7 18 31 33 3 13 12 24 25 11 5 20 16 9 27 22 14 2 23 26 10 15 34 30 6 19 17 32 4 21 28 8
Size: 35
1 35 29 7 18 31 33 3 13 12 24 25 11 14 22 27 9 16 20 5 4 32 17 19 6 30 34 2 23 26 10 15 21 28 8
Size: 35
1 35 29 7 18 31 33 3 13 12 24 25 11 14 22 27 9 16 20 5 4 32 17 19 30 6 10 26 23 2 34 15 21 28 8
Size: 35
1 35 29 7 18 31 33 3 13 23 26 10 6 19 30 34 2 14 22 27 9 16 20 5 11 25 24 12 4 32 17 8 28 21 15
Size: 35
1 35 29 7 18 31 33 3 13 23 26 10 6 30 19 17 32 4 12 24 25 11 5 20 16 9 27 22 14 2 34 15 21 28 8
Size: 35
1 35 29 7 18 31 33 3 22 27 9 16 20 5 4 32 17 19 6 30 34 2 14 11 25 24 12 13 23 26 10 15 21 28 8
Size: 35
1 35 29 7 18 31 33 3 22 27 9 16 20 5 4 32 17 19 30 6 10 26 23 13 12 24 25 11 14 2 34 15 21 28 8
Size: 35
1 35 29 20 5 4 32 17 8 28 21 15 10 26 23 13 12 24 25 11 14 22 27 9 16 33 31 18 7 2 34 30 19 6 3
Size: 35
1 35 29 20 5 4 32 17 8 28 21 15 34 30 19 6 10 26 23 2 7 18 31 33 16 9 27 22 14 11 25 24 12 13 3
Size: 35
1 35 29 20 5 4 32 17 8 28 21 15 34 30 19 6 10 26 23 13 12 24 25 11 14 2 7 18 31 33 16 9 27 22 3
Size: 35
1 35 29 20 5 31 18 7 2 23 26 10 6 19 30 34 15 21 28 8 17 32 4 12 13 3 33 16 9 27 22 14 11 25 24
Size: 35
1 35 29 20 5 31 18 7 2 34 15 10 26 23 13 12 24 25 11 14 22 27 9 16 33 3 6 30 19 17 32 4 21 28 8
Size: 35
1 35 29 20 5 31 18 7 2 34 30 6 19 17 32 4 12 24 25 11 14 22 27 9 16 33 3 13 23 26 10 15 21 28 8
Size: 35
1 35 29 20 5 31 18 7 2 34 30 19 6 10 26 23 13 3 33 16 9 27 22 14 11 25 24 12 4 32 17 8 28 21 15
Size: 35
1 35 29 20 16 9 27 22 14 2 7 18 31 33 3 6 10 26 23 13 12 24 25 11 5 4 32 17 19 30 34 15 21 28 8
Size: 35
1 35 29 20 16 33 3 13 12 4 32 17 8 28 21 15 34 30 19 6 10 26 23 2 14 22 27 9 7 18 31 5 11 25 24
Size: 35
1 35 29 20 16 33 3 13 12 24 25 11 5 31 18 7 9 27 22 14 2 23 26 10 15 34 30 6 19 17 32 4 21 28 8
Size: 35
1 35 29 20 16 33 3 13 12 24 25 11 14 22 27 9 7 18 31 5 4 32 17 19 6 30 34 2 23 26 10 15 21 28 8
Size: 35
1 35 29 20 16 33 3 13 12 24 25 11 14 22 27 9 7 18 31 5 4 32 17 19 30 6 10 26 23 2 34 15 21 28 8
Size: 35
1 35 29 20 16 33 3 13 23 26 10 6 19 30 34 2 14 22 27 9 7 18 31 5 11 25 24 12 4 32 17 8 28 21 15
Size: 35
1 35 29 20 16 33 3 13 23 26 10 6 30 19 17 32 4 12 24 25 11 5 31 18 7 9 27 22 14 2 34 15 21 28 8
Size: 35
1 35 29 20 16 33 3 22 27 9 7 18 31 5 4 32 17 19 6 30 34 2 14 11 25 24 12 13 23 26 10 15 21 28 8
Size: 35
1 35 29 20 16 33 3 22 27 9 7 18 31 5 4 32 17 19 30 6 10 26 23 13 12 24 25 11 14 2 34 15 21 28 8
Size: 35
1 35 29 20 16 33 31 18 7 9 27 22 14 2 23 26 10 6 3 13 12 24 25 11 5 4 32 17 19 30 34 15 21 28 8
Size: 35
1 35 29 20 16 33 31 18 7 9 27 22 14 2 23 26 10 6 19 30 34 15 21 28 8 17 32 4 5 11 25 24 12 13 3
Oh, and as a note, for each combination it will find two lists. For example, it will find:
Size: 32
1 8 28 21 4 32 17 19 30 6 3 13 12 24 25 11 5 31 18 7 29 20 16 9 27 22 14 2 23 26 10 15
Size: 32
1 15 10 26 23 2 14 22 27 9 16 20 29 7 18 31 5 11 25 24 12 13 3 6 30 19 17 32 4 21 28 8
Which are really the same lists, just in reverse order. Since it is a circle, order doesn't matter.
C++ code:
#include <iostream>
#include <fstream>
#include <vector>
#include <math.h>
#include <windows.h>
using namespace std;
void testVals(vector<int> base, vector<bool> use, vector<int> test);
bool compare(int x, int y);
int main()
{
int start = GetTickCount();
for (int size = 2; size <= 32; size++)
{
cout << "Testing list size " << size << "..." << endl;
vector<int> base;
vector<bool> used;
vector<int> test;
for (int gen = 1; gen <= size; gen++)
{
base.push_back(gen);
used.push_back(false);
}
testVals(base, used, test);
}
int end = GetTickCount();
cout << "Time: " << (end - start) / 1000.0 << endl;
return 0;
}
void testVals(vector<int> base, vector<bool> used, vector<int> test) {
if (test.size() == base.size())
{
bool result = compare(test[test.size()-1], test[0]);
if (result)
{
ofstream o("asdf.txt", ios::app);
o << "Size: " << test.size() << endl;
for (int x = 0; x < test.size(); x++)
{
o << test[x] << " ";
}
o << endl;
}
return;
}
for (int x = 0; x < used.size(); x++)
{
if (used[x] == false)
{
if (x != 0)
{
if (!compare(test[test.size()-1], base[x])) {
continue;
}
}
used[x] = true;
test.push_back(base[x]);
testVals(base, used, test);
test.erase(test.end()-1);
used[x] = false;
}
}
}
bool compare(int x, int y)
{
double temp = sqrt((double)x + y);
const double amount = 0.00001;
if (temp + amount > (int) temp && temp - amount < (int)temp)
{
return true;
}
return false;
}
Alright, here is the psuedo code:
Declare three arrays: base (integer), used (boolean), and test (integer)
main:
From size = 2 to size = 32 (or whatever numbers you wan't)
clear all three lists so they have 0 elements
From gen = 1 to gen = size
add gen to base
add false to used
testVals(base, used, test)
testVals: recieves arrays base (integer), used (boolean), test (integer)
if test size is equal to base size
test the list to make sure all adjacent values are perfect squares, then output if they are
return (exit the function)
else
From x = 0 to x = size of used
if used[x] == false //you have yet to use this number in the list
if x != 0 //don't compare 0 because 0 - 1 is not in the array
if compare(test[x], test[x-1]) is false // see function compare below
continue //skip all the code below, but continue in the current loop
used[x] = true
add base[x] to the back of test
testVals(base, used, test)
remove the last element of test
used[x] = false
compare: recieves x (int), y (int)
if the sqrt of x + y is an integer
return true
return false
Well since we know there are an infinite amount of primes, this isn't such a great discovery.
However, if we could find an algorithm to find every prime, it would be a great accomplishment. And the more primes we know, the easier it is to do this. Especially if we know the really high ones.
Hah! I am so stupid...
The way my algorithm works is that it builds a list of numbers, then tests them. I completely forgot that I could test them while building, and stop building them if I run into a combination that doesn't work!
My program tried all possible combinations from lists of size 2 to 32 in 0.82 seconds, and found the one at 32.
I'm doing the same Krassi. I had it done before, but I realized that a method I used to cut down on execution time just eliminated some needed tests. So I'm back to my original program. It takes O(n!) time, right now it's on size 12 and has to do 479,001,600 comparisons.
Set A is a subset of set B if for every element in A, that element exists in B.
Set A is a proper subset of set B if A is a subset of B, but B is not a subset of A.
So {Fred, Ashraf} is a subset of S because both Fred and Ashraf are in S.
But S is not a subset of {Fred, Ashraf} because Sue is not in {Fred, Ashraf}
Now take it one step further:
Prove that if A is a proper subset of B, then A is a subset of B.
Proof: For A to be a proper subset of B, A must be a subset of B.
Therefore A is a subset of B. QED.
Nope, you're just plugging in wrong.
-x^-2 = -1 / x^2
So if x = 1/2:
-1 / (1/2)^2 = -1 / (1 / 4) = -4
6 saw the movie Se7en. That would be enough for me.
pwnd should be pronounced owned, just like you don't say, "one thousand three hundred and thirty seven" (1337), you just say leet.
And no, there have been no languages which have no pronunciation because language came first, writing came second.
If x = -1, then:
y = 1 / (1 - 1) = 1 / 0
This is not 0, it is undefined. In this particular equation, it is either negative or positive infinity.
You're just unlucky with the coordinates you picked to graph it.
Try x =
1/4 - 1
1/2 - 1
1 - 1
2 - 1
4 - 1
8 - 1
Do the same for the negative side.
y' = 0.11y, where y' is the amount you get per year, y is the amount you have, and t is time (in years)
dy/y = 0.11dt
ln(|y|) = 0.11t + C
y = C*e^(0.11t)
y(0) = 3,415,569
y(0) = C*e^0
C = 3,415,569
y = 3,415,569*e^(0.11t) --> This is the equation you're looking for
y = 5,000,000
5,000,000 = 3,415,569*e^(0.11t)
e^(0.11t) = 1.464
0.11t = 0.381
t = 3.464
If you don't know calculus, don't worry about the above. If you do, just ask and I'll explain all the steps.
Edit:
Or are you saying that the interest rate is compounded daily? I'm having a little trouble understanding your wording.
Yes, but it is normally stated in a different way, and thus involving less theorms.
y = a * f(x), y' = a * f'(x)
So:
y = 3 * (x^4), where f(x)=x^4
y' = 3 * (4x^3) = 12x^3