# Is my solution to this puzzle reasonable?

Note the deadline has passed so I’m not asking you to do my homework – though I am asking you to check it.

First I assume the sat phone doesn’t have GPS nor is it a LEO system because that is too easy (since location can be determined by which satellites you hit/Doppler shift)

I say call when the sun is fully visible and say “Help I’ve been kidnapped and am on a small island surrounded by salt water and the sun just became fully visible. I will call again at sunset”

Timing dawn determines longitude, and the length of the day determines latitude. Even if these are off by a few minutes an isolated island should be findable. Scratching HELP/SOS in the sand is not a bad idea.

I may be overestimating how accurate this method of determining location is. Is the fact that it is salt water really all that important?

Thanks,
Brian

If that’s not the intended answer, you’re probably on the right track. The only problem I can think of is that your method wouldn’t work very well around the equinoxes, since the day & night length are equal pretty much everywhere on Earth on that day. Maybe the fact that you were kidnapped on a “snowy night” was supposed to preclude this, but I’ve seen plenty of snowy March 21sts in my part of the world.

It’s also not clear to me whether it was intended that you could make more than one phone call, though that’s more a question of “what is the intended answer” instead of “what is a valid answer”.

If you watch the sun rise you can make your call when it is as just past half way risen. This will give you one minute before the sun is just touching the horizon. Tell them what you know about your location, (island, its size, climate) and get them to mark your time call of the moment the sun is free of the horizon. Then you will run out of phone call. You will have established your longitude to easily 1/60th of a degree (only needs to be to within 4 seconds with the timing). That is one nautical mile at the equator. There cannot be many small islands that match the description on such a fine longitude constraint. Indeed very unlikely to be more than one.

Well, I think the rules are that you have to call by daybreak and making a second call at sunset is not allowed.

but it should be easy to determine longitude by calling them at daybreak and letting them determine your local solar time.

Since it is cool, you can estimate lattitude as temperate; when the sun rises you can determine directions. But I don’t know if this will be able to tell you if you are in the northern or southern hemisphere. Just a bit of astronomy knowledge should allow you to recognize Polaris in the sky or not … which puts you in a particular hemisphere…don’t know if that is allowed. You know the day roughly since its wintertime where you were.
Also you can determine if the tide is coming in or receding at the time of your call, so that can help.

I think those clues with a small flat sandy island would be enough to locate

the food and ‘pint’ bottles could indicate some nearby country, but I don’t think that is strong enough data to be confident

If two calls are not allowed (though it is IMHO within the contraints), my other idea is to call when your shadow is exactly X water bottles long (alternatively when it is exactly your height) – though I’d be worried it never gets that short.

Brian

I would hope and pray that I am in the Northern hemisphere, because I could give a rough estimate of latitude based on the height of the north star. I think that qualifies under “Your knowledge of astronomy is too weak to try to estimate your location by the stars, but you’re not stupid.” I do recall that my fist outstreched is roughly 10 degrees.

I thought that my rough estimate may not be good enough for rescue purposes, but if each degree of latitude is 69 miles (which I had to google), I think I could get within 500 miles of my latitude.

And then of course calling right at daybreak should give longitude more precisely.

ETA: but in this scenario I would expect not to be rescued. Getting all that info across in one minute and making someone believe it, plus the time to organize an actual rescue party from who-knows how many miles away, doesn’t sound promising.

ETAA: I could also use the water bottles to more accurately estimate the latitude. But again, in the southern hemisphere I’m screwed.

Calling at the moment of sunrise would narrow it down to an sort of north-south arc (not exactly a line of longitude, but kind if similar). Which, would I presume narrow it down to a dozen or so islands of the approximate size that are out of sight of other land. Few enough for a billionaire’s people to check?

If you could call at exactly local noon, with an estimate of the sun height (e.g. how long your shadow is), that’s going to get latitude and longitude which should do it (as an extra check you could also estimate the angle between the sunrise and noon locations).

You also know that the boat’s wake stirred up something bioluminescent: That’ll narrow down location, too.

What’s hanging me up is the “you don’t know enough about astronomy…” bit. Just how much astronomy knowledge are we assuming? Even perfect knowledge wouldn’t be enough, without access to some sort of chronometer. And knowing that you can use time of sunrise to give one coordinate is itself astronomical knowledge.

But you don’t know the exact direction of north/south to begin with, so the only way to judge the timing of local noon is by looking at the length of the shadow. It won’t be accurate at all - I think the best you can do is “it looks like it hasn’t gotten any longer in the past 10 minutes”.

Well, you got “a few” days’ worth of food and drink, no, so you could use day 1 to plot the shadow of some object, and on day 2, you should be able to know well enough where “noon” is. I don’t know if that “few days” is an important detail, but it sounds like you don’t have to call at daybreak of day 1, so perhaps that opens up some other possibilities.

While there are some good locations for regular/predictable bioluminescence (the 3 bioluminescent bays of Puerto Rico come to mind), the actual phenomenon isn’t that restricted and can occur worldwide.

I think the OP’s onto a good idea.

All else I can say is - liverwurst + peanutbutter on rye? That’s some sick torture there.

I suppose writing a message on a torn piece of shirt in blood and launching it in an empty water bottle would be too slow.

Weird thing is I read that and thought, that’s clearly trying to be a bit disgusting, but that sounds like a darned fine lunch to me! Plus reasonably calorie dense, I would think, depending on how peanut buttery and liverwursty it is.

Yeah, that’s why I wrote ‘if’. Getting sunrise fairly precisely is easier than getting noon precisely. Though you should be able to get a decent direction of the sun at noon, since it’s not changing too quickly. Mark that, then wait until sunset and call, giving them the approximate angle of sunset (compared to noon) and exact time. Which doesn’t meet the puzzle’s implied ‘Escape at Dawn’ constraint.

If you can find north/south by the stars, you can call in the morning and give the angle between N and the sunrise as well as the exact moment of sunrise, to get a rough latitude and longitude. If you have zero knowledge of constellations or stars, you’re not going to know whether you’ve found N or S, but narrowing it down to one of two spots on the globe is probably enough to get rescued.
I think the bioluminescence doesn’t narrow things down any more than ‘it’s not cold here’ does.

Assuming two phone calls are do-able, if you make the first call right at sunrise, this should give a rough longitude. If you made the second call exactly at sunset, couldn’t your rescuers figure out a rough latitude based on the “length” of the day?

yes, that was my solution in the OP

You have one minute of battery. I made the leap that two 30 second calls was OK. Will find out Friday

Brian

Yeah, but do I know how to find Polaris? If so, I can measure the distance above the horizon in “satphone units,” and then call when the Sun has just risen, which give both Lat and Lon.

You’re making an assumption about which hemisphere you’re in, there. How good are you at finding Crux and the Centauris?

The more I think about it, I think that part is more about prohibiting someone from triangulating their position based on locating Venus, Betelgeuse, the Vogon Mothership, and Delta Airlines flight 954, and referring to one’s photographic memory of almanacs and flight schedules; rather than an elementary “I see Polaris so I’m in the northern hemisphere.” I’m still a little unclear as to whether “My fist is about 10 degrees of arc, so Polaris is 25 degrees above the horizon” falls afoul of the rule. I don’t think it does.

The puzzle writer confirmed on twitter that there is no limit to the number of calls, just the time limit.