ElectricPavlov

Each square requires 4 points.....then you can rotate it by 1 point....then 1 point again.....

you can rotate 49 times before you start to repeat the square pattern.....the original square plus 49 more = 50 squares.

You're welcome!  Hope we didn't confuse you as much as I often am. 

Hmmmmm...... the question stated there is a knot (bus door essentially) so the beads CANNOT rotate......so I got 12 too.

10,000(1+.045)^2  - 10,000 = $920.25 interest after two years.

Second one:

First one:

Hey CPhil....   What about the other math book?  5 history books + 1 math book = 6 books in the middle.

Similar to how many ways can ten people line up while waitng for a bus:  10!

How many ways can 4 people (beads) line up on a bracelet?  4! = 24   BUT 1/2 of these will simply be 'reflections' and are disallowed.....so  24 x 1/2 = 12 ways.      (my guess....anyone else?)

Your keyboard seems to have a problem with the apostrophe key.

I think:

1.

There are 6 different ways a math book can be at both ends.

That leaves 6 books in the middle that can be arranged 6! ways

6 x 6! = 4320