Melody

hi Alan,

I often repeat the question first but I don't know why my calculation wasn't there as well.

Just another of life's mysteries I guess.  :))

what happened to my answer?   It has disappeared!  I must look under the bed!!!

I did have  5!/3! = 20

how annoying!

I roll a fair 6-sided die five times. How many sequences of rolls will give me three 2's, one 4, and one 6? (A "sequence of rolls" is an ordered list of rolls, like 1, 1, 2, 1, 2.)

deleted deleted

2*4! =

$${\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{4}}{!} = {\mathtt{48}}$$

Thanks Chris and Nauseated.

I shall have to have a really proper look when it is not after 3:30am   :)

I am splitting my regular octagon into 16 sectors so each one will radiate from a 360/16= 22.5 degree angle at the centre.

$$\\tan22.5=\frac{0.5L_1}{a}\\\\
0.4142\approx \frac{0.5L_1}{a}\\\\
a\approx\frac{0.5L_1}{0.4142}\\\\
a\approx1.2071L_1\\\\
also\\\\
tan22.5\approx\frac{0.5L_2}{a+2}\\\\
0.4142\approx \frac{0.5L_2}{a+2}\\\\
a+2\approx \frac{0.5L_2}{0.4142}\\\\
a\approx \frac{0.5L_2}{0.4142}-2\\\\
a\approx 1.2071L2-2\\\\$$

$$\\so\\\\
1.2071L2-2\approx 1.2071L_1\\\\
1.2071L2\approx 1.2071L_1+2\\\\
L_2\approx L_1+\frac{2}{1.2071}\\\\
L_2\approx L_1+1.6569\\\\$$

so YES for a regular octagon, if you put the 2 unit border around it like you said, the side length will increase by a set amount which is approx   1.6569 units

you want to expand and simplify?

$$\\(p+2/2)(p+\frac{7}{2})\\\\
=(p+1)(p+\frac{7}{2})\\\\
=p(p+\frac{7}{2}) \quad +1(p+\frac{7}{2})\\\\
=p^2+\frac{7p}{2}+p+\frac{7}{2}\\\\
=p^2+\frac{7p}{2}+\frac{2p}{2}+\frac{7}{2}\\\\
=p^2+\frac{9p}{2}+\frac{7}{2}\\\\$$

how about B=45

You do not have any other informations :)

I will give it a puzzle icon for now and if I like your final answer I will add it to the puzzle thread then.  OK?