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The answer is, they use the tides to work out how many of them have triangles.
OK, here’s my thinking.
We’re not told how many people are in the crowd, so let’s set that at one as a base case.If there were only one person there, then it would be easy.He can leave on the next high tide as there would be only one of him, so the sailor must have been talking to him.So,
Case 1:When number of triangles = 1, then tide to catch = 1.
But it’s not the case that there was only one – there must be more (otherwise it wouldn’t be a crowd.)
So let’s set the crowd size at two.Now both people aren’t sure if it’s them, but can see the other person. There are two possible scenarios:
1.Only one of them has a triangle.
2.They both have triangles.
NB we can rule out neither of them having a triangle because the sailor said he could see at least one.
Let’s assume (1).It follows then that:
1.Only one of them has a triangle
a.Person A has a triangle, but B doesn’t.
i.Person A can see B doesn’t, know’s that at least one person does, so it must be him.Happy days!Off Person A goes into the boat by the first tide.
b.Person B has a triangle, but A doesn’t
i.Exactly as above, B can deduce that he has the only triangle, and leaves on the first tide.
However, if neither leave on the first tide, then both can deduce that their assumption (1) is wrong.Therefore it must be (2) – that they both have triangles.Therefore they both leave on the second tide.
Case 2:When triangles = 2, then tide to catch = 2.
Likewise when we get to 3 triangles, each person can see 3-1 of them.They must wait for the 3-1 (3rd) tide.If no one leaves, he can leave on the next one with the other 2.
Extrapolating from this,
Case N: When triangles = N, then tide to catch is N.
Well done, John.As I mentioned, the prize to the person who get’s the right (or closes) is a shout-out on this page and a link to their site.Here’s his shout out.John has nominated a website which provides reviews and guides about virtual private networks.The review site covers a number of the most popular, and includes a new review about Kepard VPN.I’ve had a look actually, and it’s well worth a look.Shout out over.
Well done, and thanks to everyone who sent in their answers.
I wrote The Pacific Riddle almost two years ago. Since then it's had over 100,000 views, which is phenomenal.
Writing new riddles takes a lot of time, and lots of checking. The process I use has 4 steps.
First is to define a suitably interesting problem in either maths or (my own preference) Boolean Logic. The art of course is in how to make it 'suitably interesting'. For me this is a gut feel for the apparent complexity of the starting assumptions and the parsimony of the solution. It's got to look hard at the start, but the answer should feel right.
Once you have that initial problem and solution, the next step is to test it for completeness. How many other solutions are obvious? Too many,and the puzzle answer will feel arbitrary. If there are two or three, then that's fine. Only the first will be provided and you can hint at the other. If it's one, then great.
Of course you can never be sure if there are other solutions that you've missed until it's out in the wild.
Once you're happy with the set of solutions it's time to move it to the third step, building it into a real world scenario (or abstract it away from the real world if maths and logic to the epiphenomunal world of perceptions, if you prefer it that way round.)
This part can be quite fun. You can put in red herrings, interesting environments or odd situations. All very arty.
And then to the final step, which is to test it in the wild. Hopefully people will like it. Hopefully it won't be too easy! Hopefully you haven't made a mistake!
So that's the process I use, and I'd like your help. If you'd like to be part of group building and testing the next puzzle please leave a comment below or contact me on Google+ (link in the side bar.) Everyone who takes part will have a credit, and the whole puzzle will be under a Creative Commons "copyleft" agreement, so free to use.
There is an island in the middle of the pacific that is inhabited by only two types of people: ones with triangles in the middle of their foreheads, and ones with circles. These two tribes have lived together for thousands of years but rarely talk because there is a mystical taboo - they can never mention what they see on each
others forehead, and can never look at their own. Anyone who breaks that taboo will be killed instantly by the others.
Although they have small fishing boats, they don't have the means to leave for another island, and have understandably becoming rather irritated with each other.
However, there is hope. There is a prophesy amongst the islanders that a boat will come which is big enough to take them all off the island forever. Never to make things easy for themselves, however, the prophesy also says that only those with circles on their foreheads can go. Those with triangles must stay. If anyone with a triangle on their forehead steps on to the boat, all will be lost and the island, with the boat, will sink forever.
All is just dandy, until one day a large boat turns up. It moors up in the bay, and the single occupant comes ashore.
The people of the island all gather to welcome the sailor, excited that at last the prophesy is unfolding. Looking at the crowd for the first time, the sailor exclaims, "Heh, I can see someone with a triangle on their forehead. Way cool!"
The crowd instantly kill him.
They then stop. They look at the boat. It's far enough in that they could only leave on a high tide, and there's only one of those a day. But at least it's big - it can take 100 people. They count themselves - there are 100 of them on the island.
There's been enough bloodshed, and no-one wants to guess. But how are they to work out who goes, and who stays?