Horse Race

Question:
Given 25 horses and 5 horses in a race, find the minimum number of races needed to find top 3 horses.

Answer:
7
Step 1: divide 25 horses into 5 groups, each group a race;
Step 2: pick the horses in 3rd place from each group above, then race and suppose get A > B > C > D > E (here '>' means faster);
Step 3: pick the first 3 horses from the group containing A and first 2 horses from group containing B, run a final race.

Below is an illustration.

Use 2 Fuses to Measure Time

Given 2 fuses, each can be burned in exactly 1 hour. However, both fuses are not uniform and we have no clue which part burns faster and which slower.

Question: how to measure 45 minutes using these 2 fuses?

Answer:
First measure 30 min, and then measure 15 min.
How to measure 30 min? Light a fuse from both ends at the time.
How to measure 15 min? That's half of 30 min. So light a fuse from both ends after it has burned 30 min.

Final answer is:
1. First light 2 ends of one fuse and 1 end of the other fuse at the same time (time 0 now);
2. At the time one fuse is burned up, light the other end of the remaining fuse (30 min now);
3. When the second fuse is burned up, it's 45 min.