## Thursday, April 7, 2011

### The tiger and the lake

You are in the middle of a circular lake. At the edge is a tiger.

In this puzzle, the tiger can't swim (which is funny, because when I was looking for a tiger photo, I found pictures of tigers doing just that).  Instead, the tiger will run along the edge of the lake, doing its best to catch you.  The tiger runs four times as fast as you can swim.
You want to get out of the lake, but if the tiger is waiting for you when you reach the shore, then the tiger will seriously damage your ability to not die.  Can you get out of the lake safely?  How?
This puzzle is a classic, not original.

See the solution

SlightlyMetaphysical said...

Tigers are VERY good at swimming/killing things in the water.

I may be wrong here, but this is the first one I've even thought I could attempt:

Assuming you're starting from the middle of the lake, because if you are slightly to one side of the middle, the tiger will wait for you on that side, it's as quick for you to get to anywhere, so you'd go to the place opposite the tiger.

This would take you r distance.
The tiger has to go half the circumference, therefore r x pi.
So the tiger has 3.14 times as much distance to run as you, so you're screwed?

blahs15 said...

I don't actually know how to calculate this, but what if you always swim towards the opposite side of the lake from which the tiger is. That way, you would be swimming in a spiral motion.

Eduard said...

There is a radius r1 where we have equal angular speed and there is a radius r2 from where the swimmer can escape. r2 is just a bit bigger than r1.

Eduard said...

Sorry the invers is true. r1 is a bit bigger than r2.

miller said...

Blahs15,
A spiral pattern will only get you part of the way. Can you figure out how far you can get with a spiral without knowing the details of the spiral?

Secret SquÃ¯rrel said...

If you move toward the shore directly away from the tiger, it will have to decide to run one way or the other to get to where you are heading. You can adjust your course to always keep the tiger directly opposite the lake centre from you, until such time as your radial velocity is the same as the tiger's.

This will be when you have swam only 1/4 of the way from the centre to the edge. In fact, I suspect that mathematically you might approach this limit closer and closer without ever reaching it but you're not a point so let's say that you get there.

You've only swum 1/4 of the way to the edge so you might appear to be beaten (or is that "eaten"?). However, in the time that you can swim 0.75R (R=radius of lake), the tiger can run 3R but is 3.14R (half circumference) away from you.

So you will be able to safely get out of the lake and be safely mauled by the tiger on the shore.

Unknown said...

I couldn't figure out what was wrong with the scenario. :-)

You don't have to swim at "full speed". Nor do you have to swim on the surface. Start to swim, slowly, toward the shore opposite the tiger. When the tiger gets near-ish (within 45 degrees) to where you're going, duck under the water, change direction to a spot behind where the tiger is now and swim for your life! (You might want to do so very slowly, so you don't alert the tiger to your plans.) You probably need to aim for a spot more than 90 deg. away from the tiger, and behind it.

If you can climb onto a bough, do so. And then run for your life.

Once you make it to shore, run for your life. Or, if you're with someone, run faster than them.

There's a lot to go wrong in this "solution". :-)

Hmmph said...

In general, tigers may be very good at swimming, but in this case, this particular tiger can't swim. Am I right? Honestly, if it's a circular lake, I would just rather stay in the circle and starve to death lol. I don't know, can I throw stones at him if I can find some under the lake??