Math Is Fun Forum

A fact about 1. is that the difference between the result for two successive integers, f(n) - f(n-1), is:

which converges to +/- 1 very fast, suggesting that integers with an absolute value above 5 do not need to be checked.

Hi, unfortunately I don't have a good intuitive understanding of the answers myself I just know that the math works, by computer-generating answers and then finding equations that produce those answers.

Another thing confirmed this way is that if you want the number of combinations with a particular number x of one type sitting adjacent to each other, that is given by 3^(15-x+1) - 2^(15-x+1). So in other words, if we want to know the number of combinations with at least one male, that is 3^15 - 2^15 (which is pretty intuitive, since 2^15 is the number with males excluded). For some reason, the number with two adjacent males, 3^14 - 2^14. With three, 3^13 - 2^13.

The formula for when there are both 3 adjacent males and two adjacent females, 3^12 - 2*2^12 + 1, I must confess I don't understand at all.

As for the formula for the final answer, that involves the total number of combinations with the numbers with three adjacent males (but not two adj. females), two adj. females (but not three adj. males), and both two females and three males taken out.

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I can only tentatively reason that the answer is probably between 8,460,000 - 8,490,000 and might be close to 8,482,000. But I am no good at sorting out complex sequences.

Hi

Hi;

Hey There is no need to approximate pi, since it cancels

Hi,

Hey Monox D. I-Fly,

I don't really know how to help out with the main issue, but I did want to point out that there is something peculiar about the line of equations you wrote.
Namely, the third to seventh lines are really one half of the first two, not equal to them. The correct denominator is 2, not 4.