Amanda

How many ways are there to move from one corner of a cube to the diagonally opposite corner, in three moves, each of which travels along one edge of the cube?

Lockers are numbered with consecutive positive integers beginning with 1, and the digit 2 is used exactly 106 times (including on the last locker). What is the number of the last locker?

A four by four grid of unit squares contains squares of various sizes (1 by 1 through 4 by 4), each of which are formed entirely from squares in the grid. In each of the 16 unit squares, write the number of squares that contain it. For instance, the middle numbers in the top row are 6s because they are each contained in one 1x1 square, two 2x2, two 3x3 and the one 4x4.

What is the sum of all sixteen numbers written in this grid?

The trees in a peach orchard were arranged in a square array with N columns and N rows. To enlarge the orchard by one row and one column to make a larger square, the owner bought and planted 29 more peach trees. How many trees are in the orchard after the enlargement?

So at school we have a "book club" where we will go into groups and read a book, I'm reading Catherine, Called Birdy. We all have "roles" and mine is to:

Be The Researcher - investigates background information on topics related to the book. I'm stuck, help!

So I've been best friends with this girl for 6 years. We've been really close but now this year, this new girl came. My best friend started hanging out with her, but I wasn't bothered by that. Now some months into the school year, they're inseperable and my best friend barely talks to me anymore, and I'm always left now. They even sit at a different lunch table now! She's still friendly towards me, but doesn't treat me as a friend. I feel like that girl is just changing her - I don't have a problem with that, except with the fact that now my best friend won't leave her side. I've spent so much time feeling down about this, I need to know what to do/what to say to her. I just don't know what happened. Please help!