Harry Potter and the Sorceror's Stone

Harry was just an ordinary ten-year old boy -- or so he thought. Then one day in July he received a letter from Hogwarts School. His uncle burned the letter, but more letters kept coming.
If one letter came the first day of July, then two letters the next day, then four letters, and eight letters -- how many letters would come on the last day of July?
How many owl-delivered letters would it take to fill up your classroom?
   

 

Bertie Bott's Every Flavor Beans
Chocolate frogs
   
   

 

Hermione is very smart. In fact, she claims she can read minds -- she can guess your birthday! You take the following cards and tell her which color cards list your birthday. She will read your mind and tell you what day of the month it is.

1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31

 2
3
6
7
10
11
14
15
18
19
22
23
26
27
30
31
4
5
6
7
12
13
14
15
20
21
22
23
28
29
30
  31
8
9
10
11
12
13
14
15
24
25
26
27
28
29
30
  31
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31