Four people come to an old bridge in the middle of the night. The bridge is rickety and can only support 2 people at a time. The people have one flashlight, which needs to be held by any group crossing the bridge because of how dark it is. Each person can cross the bridge at a different rate: one person takes 1 minute, one person takes 2 minutes, one takes 5 minutes, and the one person takes 10 minutes. If two people are crossing the bridge together, it will take both of them the time that it takes the slower person to cross. Unfortunately, there are only 17 minutes worth of batteries left in the flashlight. How can the four travellers cross the bridge before time runs out?

Why this works

This riddle is a classic example of a logic puzzle that involves careful planning and the strategic grouping of people based on their crossing times. The key to solving it is to minimize the time spent by the slower crossers while ensuring that the flashlight is always with the people crossing. Here's how the solution works: First, the two fastest individuals (1 and 2 minutes) cross the bridge together, allowing them to return quickly. Then, the two slowest individuals (5 and 10 minutes) cross together, which takes the most time but is necessary to use the flashlight efficiently. Finally, the fastest one returns to escort the two faster individuals back across the bridge, ensuring all four make it in exactly 17 minutes. The logic hinges on balancing the time spent crossing with the need to have the flashlight at all times, creating a clever sequence that adheres to the limits of the riddle.