FOUR CYCLISTS A,B,C&D WANTS TO CROSS A BRIDGE BUT DUE TO BAD CONDITION OF BRIDGE ONLY TWO AT A TIME CAN CROSS IT. IF A TAKES 1 MINUTES, B TAKES 2 MINUTES,C TAKES FIVE MINUTES & D TAKES 10 MINUTES TO CROSS THE BRIDGE, HOW THEY ALL CAN CROSS THE BRIDGE IN 17 MINUTES. IF ONE LAMP IS AVAILABLE TO CROSS THE BRIDGE.
- A & B cross the bridge (2 minutes)
- A go back with the lamp (1 minute)
- C & D cross the bridge with lamp (10 minutes)
- B go back with the lamp (2 minutes)
- A & B cross the bridge with lamp(2 minutes
To solve this problem, we need to find a way to get all four cyclists across the bridge within the given time constraint of 17 minutes. Here's one possible solution:
Step 1: A and B cross the bridge together.
- Time elapsed: 2 minutes
Step 2: A goes back with the lamp.
- Time elapsed: 3 minutes
Step 3: C and D cross the bridge together.
- Time elapsed: 13 minutes
Step 4: B takes the lamp and goes back.
- Time elapsed: 15 minutes
Step 5: A and B cross the bridge together.
- Time elapsed: 17 minutes
Explanation:
Initially, we can send any two cyclists with the lamp, and since they take different amounts of time to cross, we should send the two fastest: A and B. This takes 2 minutes.
To ensure that there is a way to bring back the lamp, A goes back alone with the lamp, taking an additional 1 minute. Now, we have C and D left on the starting side of the bridge.
We need to find a way to bring C and D across the bridge, but since D is the slowest, we can't send him alone. Instead, we can send C and D together, which will take 10 minutes in total.
Now, we need to bring back the lamp to the starting side, and since B is already on the other side, he can take the lamp and come back in 2 minutes.
Finally, A and B can cross the bridge together, taking 2 minutes to reach the other side. So, in total, it takes 17 minutes to get all four cyclists across the bridge.
Note: This solution assumes that the lamp is needed to cross the bridge, and only two cyclists can cross at a time due to the bad condition of the bridge.