Puzzle 8 The Path to Justice

Lucas Bachmann

The solution to the previous puzzle can be found here.

If you’ve missed any of the story so far, you can catch up on all of the puzzles here.

And voila, the trap is set. Now all that is left is for the men to come out.

“Let’s trigger one of the alarms, see if they come out” Bernoulli stated.

Hansel nodded, and stepped on one of the pressure pads. Instantly, a blaring siren could be heard. A large commotion in the following room ensued, followed by a large bang of the door. The three men walked out, but unfortunately for them, the door had set the trap into action, and the fishing net soon fell on them. Two of the men were completely trapped by the net, and were desperately trying to squirm their way out. The third man was more lucky, and managed to dash in between Bernoulli and Hansel, and was quickly running away.

“Secure the crime scene, detective, I will handle the perpetrator!”

And with that, Hansel was gone. Bernoulli went to the two men, and handcuffed them to the wall with little resistance. He peered into the next room to find a printing press, still churning out bills, and several bags of money, identical to the ones in the bank.

His phone started ringing. It was Hansel.

“Hello Constable, did you catch him?”

“Yes, I have managed to arrest the man. However, I am now completely lost. Plus, the thief dropped something while he was running, which I didn’t pickup. It would be really helpful if you could help me find the path I took”

“No worries, Constable”. Bernoulli walked towards a table, where he spied a map of sorts. “I have found a map of the port. We can retrace your steps and figure out where you’ve gone”

“Sorry detective, I do not remember much about my journey. All I know is that I ran for exactly 17 minutes without stopping, and whenever there was a fork in the road, I ran through without a pause. In fact, I am at a fork right now. The other thing I know is that I never went down a street twice”.

“Let’s see here”. Bernoulli studies the map “I do know how fast you can run. Thus, I can write down how long it takes you to travel from one fork in the road to another. Then, all I need to do is find all of the paths that takes 17 minutes to travel. You are bound to be at the end of one of them.”

Starting from the red spot, can you find a path of length exactly 17 where no street is used more than once?

Scroll down for solution…

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Solution

Very quickly, Bernoulli circles an intersection on his map, and runs to catch up with Hansel. Hansel, impressed by Bernoulli’s incredible speed, asked “how did you find me so quickly?”

“Well,” Bernoulli replied “I noticed that my map had a certain peculiar property: almost all of the paths on the map would have taken exactly an even number of minutes for you to travel. Since you travelled an odd number of minutes, you must have gone on a path with an odd travel time an odd number of times. If that is the case, then you must have ended up here,” Bernoulli pointed to this location, the lower right fork on the map “as all odd paths end up here, and there is no way of leaving this fork without travelling down another path of odd travel time. After that, it wasn’t hard to find a path that would have taken you 17 minutes to travel.”

And the case is solved! Thanks to your help, the criminal masterminds have been apprehended, and the money recovered. Another job well done for Detective Bernoulli and Constable Hansel!

If you’ve missed any of the puzzles in the series, you can find them all (with solutions) here.

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