Leo's Magic Number

Leo has a magic number ABCDE that satisfies the following conditions:

1. ABCDE = FD × HI × GB;
2. HI × GB = DGBE;
3. FD, HI and GB are prime numbers;
4. A, B, C, D, E, F, G, H, and I are nine different single-digit non-negative integers.

What is Leo's magic number ABCDE?

Counting Trails

48 Charlotte Math Meetup students have a meetup together. Each holds a square tile of 1 m². They put the tiles together to form a big rectangle of 48 m². Leo tries to complete a trail from the bottom left tile to the top right tile. (The trails are not along the edges of the tiles, but from one tile to another tile.) If every time he can only go up or right, and if the students try to make the rectangle such that there are as many trails as possible. what’s the most number of trails?

Adding Square Roots

Calculate:

  .

3x3 Basketball Teams

Leo and 8 other kids are shooting around in the gym. They decide to play 3x3 pickup games. They want to split up in to 3 teams, with 3 players on each team. How many different ways can they split the group?