In the’Riddle of the bridge There are Four peoplesome slower and others faster, who to escape a horde of zombies must cross, in the darkness of the night, a dangerous bridge that holds up at most two people at a time. They only have available 17 minutes To save themselves, before the zombies reach them.
Considering that the bridge is dangerous and cannot pass all together, will they be able to save themselves in 17 minutes having only one torch available? Let’s see the solution to the indovinel of the bridge.
Description of the Ponte Indovinello
It is a dark summer night, you are on an island with friends and you are returning home after a beautiful day at the sea when, from a dark cave, a horde appears zombie which aims precisely towards you. The only way to save you is cross the rope bridge That connects the island to the mainland and then cut the ropes so that the zombies remain on the island.
Marta, the group’s nerd, calculates you exactly 17 minutes To cross the bridge before the zombies reach you, but The bridge holds a maximum of two people at a time And you are four: the sportsmen Larissa and Mattia, the nerd Marta and the careless Edo who just that morning put a foot on a sea urchin and cannot walk well. For this, each of you has different travel times:
- Mattia The sportsman uses 1 minute
- Laissa It is also very quick: 2 minutes
- Marta It is a little slower with 5 minutes
- Edo, which is injured, 10 minutes
There is still a problem though, You have only one half a downloadso when Two of you cross the bridge must do it at the speed of the slowest of the two and, once you arrive, Someone will have to bring the torch back to his companions remained on the other side. For example, if Edo and Larissa cross the bridge first they will take 10 minutes and one of the two will have to go back to bring the torch to the rest of the group.
How can you do to cross everyone the bridge in 17 minutes and save yourself by cutting the ropes?
To help you reflect us, we summarize the key points:
- The bridge can be crossed by a maximum of 2 people at a time;
- The 4 friends have different travel times;
- You have only one torch;
- Two friends who cross the bridge are forced to do it at the speed of the slowest of the two to prevent one from remaining in the dark;
- You have 17 minutes of time.
The solution to the poverty of the bridge
The first thing that almost everyone thinks is that, to waste as little time as possible, it must be the fastest of the group to instruct the torch to the starting point. For example, one could proceed as follows:
- Edo and Mattia cross the bridge in 10 minutes
- Mattia reports the torch: and we are at 11 minutes
- Mattia and Marta cross the bridge in 5 minutes: and we are 16
- Mattia reports the torch and we are at 17
- Mattia and Marta cross the bridge in 2 minutes: we are at 19, too late!
Something went wrong, but what? The fact is that this riddle has two types of problems, one easier to see and the other a little more hidden.
First of all when we report the torch back we waste time, so At the end of the bridge there is always someone quick enough to bring the torch back back Losing as little time as possible. The best candidates for this task are Larissa and Mattia: it must be made that at the end of the bridge there is always at least one of the two ready to bring the torch quickly back.
The second problem is that when one of the two slowest friends are lost to cross the bridge, a lot of time is lost. If Marta and Edo travels separate use a total of 15 minutes, which is almost 17, the maximum allowed. The way to Avoiding this waste of time is to make Marta and Edo travel togethertaking 10 minutes instead of 15.
Keeping in mind these two observations we can see a solution of the indovinel:
- Larissa and Mattia cross the bridge first: we are a 2 minutes
- Mattia goes back with a torch in 1 minute: we are a 3 minutes
- Marta and Edo cross the bridge in 10 minutes: we are a 13 minutes
- Larissa brings the torch back to Mattia in 2 minutes: we are a 15 minutes
- Mattia and Larissa cross the bridge in 2 minutes: We are at 17.
The four friends arrive just in time to cut the rope bridge before the zombies arrive.
What we have proposed is one of the optimal solutions to this problem, in the sense that there are no better solutions in which the 4 friends take less than 17 minutes. If desired you can try all the possible combinations, it is a strategy allowed in mathematics, only that if there are many possibilities, you risk not succeeding, so it is convenient, as we did, identify the crucial points of the problem and start from those.
Now that you have understood, you can also reformulate the riddle by changing characters and numbers, for example:
What would be the minimum time necessary to cross the bridge if the travel times of the four friends were 2 minutes, 3 minutes, 9 minutes and 15 minutes?
Spoiler, it’s a perfect square!
