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 (3^{rd}) 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.