Alan

I don't have a formula for this, but I ran a Monte-Carlo simulation for it.  This doesn't give an exact answer, but gives a ball-park figure.

I repeatedly selected 6 numbers in the range 0 to 252 at random, and kept count if their sum totalled 508.  

I did this 10⁷ times.  In around 9000 of these 10⁷ trials the sum totalled 508.  The total number of possible ways of allocating 0 to 252 to the 6 stats (without regard for their sum) is 253⁶, so the likely number of possible ways of allocating 508 points to 6 stats such that no one stat has more than 252 points is approximately (9000/10⁷)*253⁶  or about 2.3x10¹¹  or 230 billion.

There and back once is 6 and 4/5km

So there and back twice is 12 and 8/5km or 13 and 3/5 km

$$3\times10^2m+5\times10^2m=(3+5)\times10^2m=8\times10^2m$$

The width is just the area divided by the length.

This can be written as

$$2x+\frac{x-1}{2}=\frac{5x-3}{3}\\\\
2x+\frac{x}{2}-\frac{1}{2}= \frac{5x}{3}-1\\\\$$

Add 1/2 to both sides and subtract 5x/3 from both sides

$$2x+\frac{x}{2}-\frac{5x}{3}=-\frac{1}{2}$$

Collect the x terms over a common denominator

$$\frac{12x+3x-10x}{6}=-\frac{1}{2}\\\\
\frac{5x}{6}=-\frac{1}{2}$$

Multiply both sides by 6/5

$$x=-\frac{3}{5}$$

9x - 2y = 25     ...(1)

4x - 5y = 7      ...(2)

Multiply (1) by 5 and (2) by 2

45x - 10y = 125     ...(3)

8x - 10y = 14        ...(4)

Now both equations have the same number of y's so we simply subtract (4) from (3) term by term:

37x = 111

x = 111/37 = 3

Substitute this back into (2)

4*3 - 5*y = 7

12 - 5y = 7

Subtract 12 from both sides

-5y = -5

so y = 1

3p + 3q = 15        ...(1)

2p + 5q = 14        ...(2)

Divide the first equation by 3

p + q = 5

Rewrite this as q = 5 - p   ...(3)

Substitute this into (2)

2p + 5(5 - p)  = 14

Multiply out the bracketed term

2p + 25 - 5p = 14

Collect the p's and subtract 25 from both sides

-3p = -11

Divide by -3

p = 11/3

Substitute this into (3)

q = 5 - 11/3

q = 4/3

ln(a^b) = b*ln(a) even if b is a fraction, so ln(a^(3/2)) = (3/2)*ln(a)

If n is the number if days, then 0.01*2ⁿ = 10⁶

Divide both sides by 0.01

2ⁿ = 10⁸

Take log to the base 2 of both sides

$${\mathtt{n}} = {{log}}_{{\mathtt{2}}}{\left({{\mathtt{10}}}^{{\mathtt{8}}}\right)} \Rightarrow {\mathtt{n}} = {\mathtt{26.575\: \!424\: \!759\: \!098\: \!9}}$$

So it takes 27 days!

The volume is height*length*width so just multiply your three numbers together using the calculator on the home page here.