Once upon a time, a family with mom, dad, son and daughter was travelling in a dark night. They had only a single torch.
It takes \(2\) minutes for the son to cross the bridge, \(3\) minutes for the daughter, \(5\) for mom and \(10\) for dad.
Only two people can cross the bridge at the same time, else it will break. If two persons are going at the same time, the time it takes for them to cross the bridge is the time it takes for the slower one to cross the bridge.
(For example, if mom and dad are crossing the bridge at the same time, it will take \(10\) minutes)
Once the torch crosses the bridge, someone must bring it back if there are still people waiting to cross.
What is the minimum number of minutes it takes all four of them to cross the bridge?
Details and Assumptions: