How to Escape a Monster Using Calculus

Nick Berry of DataGenetics poses a puzzle of logic, strategy, and math. Since Halloween is coming up, it involves a monster. I think he's kind of cute, but that's not the point at all. He will eat you if he catches you!

Imagine you are sitting in a rowing boat in the middle of circular lake. Standing on the edge of the lake is a hungry monster. The monster wants to eat you. You want to escape.

You know that, if you can reach land, you can outrun the monster, but first of all, you need to row to shore. Here’s the issue: whilst you can outrun the monster on foot, he can run faster than you can row the boat. Much faster. The monster can run four times faster than you can row. He’s also a clever monster and will always do that smartest thing to attempt to catch you; moving around the shoreline, as needed, to maximize his advantage. If he touches you, you’re dead!

Can you escape?

Knowing how circles work and knowing that pi is less than four, rowing straight for the shore opposite the monster will not help you. For the purpose of this game, you cannot do something odd like jump out of the boat and swim, or call 911 for a helicopter. Yes, there is a way to do it. I was tempted to take his word for it, thinking I'd never understand the math involved, but as Nick explains the solution, it makes sense even if you didn't study calculus. Try to figure it out on your own first, then read the winning strategy at Datagenetics.

But wait, there's more! What if the monster could run even faster? Nick wondered exactly how much faster a monster would have to run than you could row to make it impossible for you to escape no matter how much calculus you used.

The fastest monster we can escape is determined when the monster arrives at the shore at exactly the same time we do. Let's define the ratio of our two speeds by the letter K. (The monster runs K-times faster than we can row). What is the maximum value for K?

Well, that involves more math, but the answer is there.

Check out previous wizardry from Datagenetics.

Love games and puzzles? Visit NeatoPuzzles for more!

Comments (1)

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Wow, that was actually pretty interesting and a good use of trig. I will admit that the more complex derivation was more than I wanted to swallow right now, but the initial solution was very interesting.
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While I understand the reasoning, it's not advised to drive with one hand on the stick áll the time. Only when actually shifting.
Even more so, it's not necessary all the time either. On a highway you have to shift to the highest gear, keep both hands on the wheel and both eyes on the road.

Where I'm from, driving stick is taught as a standard.
If drivers don't show to be sensible in the way that you simple "can't" do anything else with your hands but driving when driving, they shouldn't be in the first place. This goes for all ages.
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Many moons ago, when I learned to drive, if you took your test on an automatic you had a restriction put on your license. And people who could only drive an automatic were scoffed at.
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Where I live, driving stick is typical, and that's what I drive. Shifting gears is only demanding for so long; after a while, your brain gets trained enough that it's part of driving, just like everything else. While a nuisance when you need a free hand, there are solutions around, even while driving through busy city traffic (where you need to fiddle with the stick a lot more than on longer trips, as Barking_Bud correctly pointed out above).

Having said all of the above, I totally recommend a teenager's first car should be manual transmission. Having to switch gears manually really helps you get an intimate feeling for how things work inside the engine, when you can expect power and when you shouldn't, and generally how to take advantage of a car's engine.
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Er, take it from someone who lives in the UK (where stick shift is the norm) this would NOT do anything to stop teenagers being teenagers. Best one I saw here was an idiot rolling a cigarette while steering with his elbows! The real answer is to make teenagers drive little electric 2 person bumper cars until they are 28 (when their brains suddenly get into gear).
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My kids want to learn to drive a stick shift. But our manual truck died, and a decent affordable used car with a stick shift is very hard to find these days. In all honesty, I'd rather have a 30-40 year old car anyway because you can repair them at home. Too bad those are considered "antique."
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I hope this push for manual does take off. In addition to reducing texting while driving, it might also introduce more people to how enjoyable it is to actually operate a vehicle, to enjoy driving rather than just seeing it as a way to get from Point A to Point B.
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