The problem of train crossing the bridge is one of the classical mathematical logic problems. Suppose there are n people who need to cross a wooden bridge, and each person has different time to cross the bridge. At the same time, there can only be two people on the bridge, and you must have a flashlight to cross the bridge. Now let's analyze the solutions in eight cases:

1. Two people cross the bridge, and the crossing time is the time of the slower one.

Solution: Two people cross the bridge together. The faster person returns to the origin with a flashlight, and then crosses the bridge with another person.

2. Three people cross the bridge, and the crossing time is the time of the slowest of the three.

Solution: Let the fastest two people cross the bridge first, one of them returns to the origin with a flashlight, and then cross the bridge with the slowest person. After that, one of the two fastest runners returned to the origin with a flashlight, and then crossed the bridge with the rest.

3. Four people cross the bridge, and the crossing time is the slowest time for two people.

Solution: Let the fastest two people (A and B) cross the bridge together, and A will return to the origin with a flashlight. Then send the slowest two people (C, D) across the bridge, and B will return to the origin with a flashlight. Finally, A and B cross the bridge together.

4. Five people cross the bridge, and the crossing time is the time of the slowest person.

Solution: Let the fastest two people (A and B) cross the bridge together, and A will return to the origin with a flashlight. Then send the person with the third shortest crossing time (C) to cross the bridge. Then one of the two fastest people (B) returned to the origin with a flashlight and crossed the bridge with the fastest person (A). Finally, A and B cross the bridge together.

Six people cross the bridge, and the crossing time is the slowest time for two people to cross the bridge.

Solution: Let the fastest two people (A and B) cross the bridge together, and A will return to the origin with a flashlight. Then send the person with the third shortest crossing time (C) to cross the bridge. Then one of the two fastest people (B) returned to the origin with a flashlight and crossed the bridge with the fastest person (A). Finally, A and B cross the bridge together.

6. Seven people cross the bridge, and the crossing time is the time of the slowest person.

Solution: Let the fastest two people (A and B) cross the bridge together, and A will return to the origin with a flashlight. Then send the person with the third shortest crossing time (C) to cross the bridge. Then one of the two fastest people (B) returned to the origin with a flashlight and crossed the bridge with the fastest person (A). Finally, A and B cross the bridge together.

7. Eight people cross the bridge, and the crossing time is the slowest time for two people to cross the bridge.

Solution: Let the fastest two people (A and B) cross the bridge together, and A will return to the origin with a flashlight. Then send the person with the third shortest crossing time (C) to cross the bridge. Then one of the two fastest people (B) returned to the origin with a flashlight and crossed the bridge with the fastest person (A). Next, take the remaining two people (D, E) who have the shortest crossing time to cross the bridge together, and B will return to the original point with a flashlight. Then cross a and b together.

8. Nine people cross the bridge, and the crossing time is the slowest time for two people to cross the bridge.

Solution: Let the fastest two people (A and B) cross the bridge together, and A will return to the origin with a flashlight. Then send the person with the third shortest crossing time (C) to cross the bridge. Then one of the two fastest people (B) returned to the origin with a flashlight and crossed the bridge with the fastest person (A). Next, take the remaining two people (D, E) who have the shortest crossing time to cross the bridge together, and B will return to the original point with a flashlight. Finally, cross A and B together.

Matters needing attention in train crossing bridge

1, pay attention to the control of time: in the process of solving problems, always pay attention to the time required for everyone to cross the bridge and arrange their own action sequence reasonably. Ensure that people who cross the bridge can complete the task in the shortest time and avoid wasting time.

2. Ensure safety: when considering the number of people crossing the bridge every time, ensure that the number of people on the bridge does not exceed the bearing capacity of the bridge. At the same time, we should also pay attention to the use of flashlights, so that people carrying flashlights are always on the bridge to ensure safe passage.