On Friday I posted this puzzle….

The Wiseman Steamship Company has a great reputation for punctual sailings. Every day at noon (Greenwich time) one of its ships leaves Southampton for New York. At exactly the same moment another ship leaves New York for Southampton. The crossing, in either direction, takes seven days and follows the same course. So, whenever a ship leaves either Southampton or New York, another ship is just docking there having arrived from the opposite direction.

You are lucky enough to get a ticket to travel Southampton to New York, how many Wiseman ships will you meet during your voyage to New York?

If you have not tried to solve it, have a go now. For everyone else the answer is after the break.

You meet all of the ones that have already set out and all the ones that set out during your journey – 15 in all!

Did you solve it?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called **PUZZLED** and is available for the **Kindle** (UK here and USA here) and on the **iBookstore** (UK here in the USA here). You can try 101 of the puzzles for free here.

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I was thinking 13. My methodology was right, but I guess I was (and still am a little) confused on the timing wording to get 16 total ships and not 14.

You miss the two that are in the harbour, waiting for a day.

I too think the logical answer is 13.

Say I am leaving on the date 8th. The one which left New York on 1st, is taking docking precisely at the same moment when I am leaving. So I do not ‘meet’ it. Likewise, when a ship would leave New York for Southampton on 15th, precisely at the same moment I would be touching New York and hence again I would not ‘meet’ that one. Hence I would only meet the ships which left New York between 2nd to 14th (both dates inclusive) and hence total 13.

The two in the harbor were what I was wondering about. I guess the tricky wording is that the “crossing” takes seven days. The riddle doesn’t say anything about how long you’d actually be on the boat, though, which would be eight days.

Can someone please help this confused woman? I got 6 as the answer because I thought I’d only meet the ones that are coming from the other direction. The ones that are coming from the same direction as you will always be either ahead of you or behind you and if only one ship leaves each day then you’d only see one ship from each day that leaves from the other direction during your 7 days journey.

Sorry scratch that my brain was damaged

I was nearer to your original answer and I’m still a bit stuck on this. I assumed that it was a one way trip taking 7 days and that one (and only one) ship would leave New York each day. That would give 7 (or 8 if you counted the one ready to leave dock as you reached New York). What am I missing?

Oh hang on…I’m missing the 7 that were already en route. Doh!

Sure, and got that solution.

There are several ways to convince oneself that this is correct, such as:

(1) with a bit of handwaving: the travel time is 7 days at velocity v, but the relative encounter velocity is 2v, hence, 14 meets, plus 1 at the other port (fencepost counting).

(2) draw a diagram of s (the position along the course) vs. t (time) for all ships. You get a diagram that looks like a trellis work. For one particular crossing, there are 13 meetings en route plus 2 at the ports.

Oh, and I believe the fleet must have at least 16 ships, since the departure frequency is 1/day, and the round trip time is 16 days, being 2 x 7 days crossing, plus 1 day at each port (by necessity and schedule).

a 16th ship would still be met somewhere in the crossing, so It doesn’t need to exist exept maybe as a replacement for breakdowns

sorry, did you mean (like Tort below) to include the ship you’re on?

Meh…was wrong with my 8 ships.

Yes, but how far apart are the flagpoles?

I got it! I am happy about that, because I did not check my answer after I figured it once.

This was my method: (you are in ship 0)

__1__2__3__4__5__6__7

0(waiting)______________8(waiting)

_15_14_13_12_11_10__9_

After 3 days:

__4__5__6__7__8__9_10

3(waiting)______________11(waiting)

__2__1__0_15_14_13_12_

When you arive:

__9_10_11_12_13_14_15

8(waiting)______________0(waiting)

__7__6__5__4__3__2__1_

You meet all the fifteen ships.

I got 16 because I counted the ship you are on. I thought that was the trick.

Precisely. The voyage starts when you’re leaving your home, so after arriving at the port you’re meeting two ships at once and then board one of them.

The answer is 16.

still like my original answer – Just the one…

on the exact “same route” – you collide and sink with all hands….

It was foggy when I took the journey so I only saw 3 ships.

Kike yyours the best! Made me smile.

Meant to say-liked your reply the best-made me smile. So ssorry,embarrassed-ccould nnott find way tto cancel or erase previous answer. Hurt arm ssso ttyping witth one finger on husband’s cheap,fluky new keyboard.

Is it that her legs aren’t really crossed?

I got 8 and still don’t get why you would meet those ahead and behind going in same direction. Can anyone enlighten me?

anonymous: you don’t meet the ones behind you.

You meet the ones which are already on their way back from New York, and you also meet the ones which are on their way from Southampton to New York at the time you leave (because by the time you reach New York, they will turn around and start heading to Southampton)

15 includes the one that docks at the moment you leave, and the one that leaves the moment you dock. 13 and 15 are equally valid answers depending upon whether you think that you “meet” these ones at the start and end of your journey. Had the journey been 6d23h59m, the answer would clearly have been 13. Had the journey been 7d00h01m, the answer would clearly have been 15. But then of course our Richard doesn’t like things clearcut.

Surely you’d be ON your boat before it was due to leave? The boat arriving at midday (if you were in Southampton) would come past you as you were getting ready to depart!

I didn’t pass any ships, I went by plane instead

Unless your plane flew east, across the whole of Europe, Asia, and the Pacific Ocean, you presumably still passed the ships!

Ok I’ll rephrase it I didn’t meet any ships unless you’ve managed to make a large ocean going liner float in the air

To solve:

1. You clearly meet a boat exactly half way due to symmetry, hence at 3.5 days into your journey.

2. There’s a day’s interval between each boat passing a fixed spot but, because you are both moving, your speed and their speed combined means that you’ll meet a boat every half-day.

3. Count forwards and backwards in half-days = 13 (or 15 if you count extremes).

Call the moment you depart “Time Zero”.

Label the ships. The ship you share the harbor with at your departure is T-7, because it departed New York 7 days before Time Zero.

The ship you see leaving New York the moment you arrive is T+7, because it is leaving 7 days after Time Zero.

There are 15 ships between T-7 and T+7, inclusive (don’t make a “fencepost error”).

Thus you encounter 16 ships (15 that you pass, plus the one that you’re on).