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dr chutney
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United Kingdom
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Actually Stan's solution requires hardly any memory. If they have a rest switch which is programmed to kick in every hour, and they always travel East, then when a parachute is located there is a rest switch override. If the parachutes have beacons the robots don't have to think as such. Everything just happens.

I'll have to wait now for the ultimate solution as I'm off on holiday. I'll know what to do if I come across any long East West roads though.
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Nir Dahan
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Munich, Germany
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Tomas,

the timer that counts down how long the bot has to travel and how long it has to wait, is the memory element.
we assume that the program itself does not hold memory - it is the "counting" elements we are interested in.

Nir
stanalger
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St. Louis, MO
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No one ever did post a zero memory solution, so I'll give it a try.
Both bots travel east at the same constant speed. They meet when an infinite
amount of time has passed.
Nir Dahan
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Stan,

my solution is just to perform random walk on one of the bots - this is sure to cover the entire track in infinite time.

nir
stanalger
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St. Louis, MO
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Ahhhh! Very good. The other bot just sits and waits.
Luckily the bots can only move in two directions. If they were not
constrained by the tracks, i.e. if they had true two-dimensional freedom,
fixing the position of one bot and sending the other on a random walk
would not work.
TomasB
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Sweden
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How is the random walk done without measurement of time or distance? I have trouble envisioning the actual program without any counter up (or down) to (or from) a random number.

Nir spoke of a one bit solution and I think I have an idea for one. Since you are not allowed to use memory to measure time or distance there could be a sensor on the robot detecting a giver (like a magnet or something) affixed at one spot on a wheel. With a single bit counting you can get that magnet to pass the sensor twice when the robot goes east and then change direction. But the program should only allow the sensor to react once when he travels west before changing direction again. And of course ignore the sensor completely after the parachute is found.

/Tomas
TomasB
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Sweden
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I came up with a followup puzzle for the first solution where they travel for some time, then stop for some time to cut down the average speed.

What should the ratio between the time they travel and the time they pause be for them to find eachother the quickest? If indeed there is such a ratio independent of where they land...

/Tomas
Heinz Weber
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Austria
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Maybe I have a solution without the need for any memory:

set the value of '1 hour' in stanalgers solution to 'as fast as possible', so they need no memory for time measurment. The robots travel each at approx half of their maximum speed to the east, and if one robot finds the parachute of the other he changes to maximum speed.

Where is my error?
Heinz Weber
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@TomasB:

I think there is such a ratio and it should be 1:1. They meet after 4*distance/speed. Right?

That's a nice one!

Heinz
TomasB
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Heinz, very good indeed on both accounts. Nice that there actually is a solution independant of where they land, isn't it?

/Tomas
Heinz Weber
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Austria
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Tomas,

sometimes the question is tougher than the answer, and that's the case here. I didn't even assume there may be an optimum, I didn't see it coming so to say. Once you formulated the question it was just calculating...
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