## Double Cross: Math Puzzle

A steamship company is famous for the unfailing punctuality of its sailings. Every day at noon, Greenwich time, one of its liners leaves Southampton for New York and exactly at the same hour, also Greenwich time, another boat sails from New York to Southampton. The crossing, in either direction, takes seven days. Thus, whenever a ship departs either form New York or from Southampton, another ship its just docking there, having arrived from the other direction. The eastbound and westbound liners ply the same course.

If you board such a vessel at Southampton, how many ships from the company do you meet during your voyage to New York?

*Thanks to Suineg for submitting! If you can figure it out, answer below in the comment section. Will reveal all in about 2 days. *

falwan| Profile October 14th, 2008 - 1:19 amAt mid way;after three and a half days,first ship is met,,,

Then one ship every half day…

that makes 7 ships without the one just moving from NewYork.

or 8 with the ship that is just leaving NewYork upon arrival.

bilbao| Profile October 14th, 2008 - 10:29 amEvery half day you meet a new vessel + the ship you meet when you depart, makes a total of 15.

michaelc| Profile October 14th, 2008 - 3:13 pmNeat puzzle suineg!

The short answer… 15.

It’s a 7 day journey with one day of docking, 2 ways. So there are 16 ships in all to complete the deliveries at a minimum (no down time for these boats).

Now, when the first ship leaves harbor, the last ship (which is 1 day behind you) is docking. Across the water every single ship is passed with exception of the ship that is 1 day ahead of your ship that left Southampton. That ship that is 1 day ahead is met at the New York dock leaving when you are arriving.

Now those in the picture you wouldn’t think would be quite that punctual!

Ari| Profile October 15th, 2008 - 2:25 am18

sebbie3000| Profile October 15th, 2008 - 3:47 amWell, and I’m rather simple here, so please don’t point and laugh, I think it would have to be 12 (including the one just docking in Southampton on the day of departure, and the one just leaving New York as it arrives).

Diego| Profile October 15th, 2008 - 11:39 amYou will encounter 1 vessel every day at noon during your voyage, supposing you leave the first day of the month you will encounter 1 vessel arriving at port, then another the second of the month and so on until the eighth of the month when you arrive at your destination, also encountering another vessel about to sail when you arrive, so:

8 vessels

lil_b7717| Profile October 15th, 2008 - 1:19 pm9 ships

lil_b7717| Profile October 16th, 2008 - 7:09 amnevermind its 8

misha| Profile October 16th, 2008 - 9:11 amFifteen.

Think of the distance between the cities as a line. One end is the 12:0 start, and the other end is the 12:00 end seven days later. There are six “nodes” in between, representing 12:00 on a day during the voyage. Think of the ships going from node to node Every time the ship arrives at a node it meets a ship going node-to-node the other way. Eight nodes, eight ships. However, as the ship passes between nodes, it will pass a ship going between nodes in the opposite direction. Eight nodes, so seven spaces between them, for a total of fifteen ships passed.

davidpw97| Profile October 17th, 2008 - 2:29 amI also believe it is 15.

Including the one arriving as you leave, you meet the 7 ships that left each of the 7 days prior to when you do. Including the one leaving as you are arriving, you meet the 7 ships that leave the 7 days after you. Lastly you will meet the 1 that leaves the same day as you.

7+7+1= 15.

suineg| PUZZLE MASTER | Profile October 17th, 2008 - 7:59 amHello everyone I will give one day more to reveal the answer, so that anyone who want to post would have the chance to put his version of the answer, cool, Tomorrow I will send the answer to RK.

RK| Founder | Profile October 19th, 2008 - 8:33 pmthe official answer to the problem is 15.

Suineg notes that “from the problem you can deduce that the company has in total 16 ships and that you pass all of them but yours.” Several good explanations are given; however he divided the problem in stages by days:

“day 0: 1 ship( the one that is arriving)

now from day 1 to 7 you see 2 ships, one in the middle of the day journey and one at the end so there are 14 ships

14+1= 15 ships

also you can solve it by a time line;I think somebody used that strategy, cool.

for the ones that put 8 vessels I think they only count the ships that were in opposite direction from our vessel, they did not count that we were going to meet the ones that depart seven days before us in they way back.

Ari put 18, cant say anything because there was no explanation in that comment, but cool. ”

Much Thanks, Suineg!

sebbie3000| Profile October 21st, 2008 - 4:51 amI don’t want to sound childish, but in your question you use ‘meet’ (which I took as ‘pass’, but in your answer you used ‘see’. Those to me are entirely different – on your voyage you don’t pass/meet every ship you see, so the answer would be different. At least, in my logic that works…

suineg| PUZZLE MASTER | Profile October 21st, 2008 - 9:16 amsebbie3000, with see I mean the same as pass because you see them while passing next to them, you pass two ships every day so 7 days X 2 ships= would be 14 ships + 1 the ship that is arriving while you are leaving your harbor (day 0 for me) equals 15, sorry by the confusion in my previous comment, but you really pass 15 ships during your voyage, cool see ya.

grimdeathwh| Profile November 2nd, 2008 - 9:56 pmI’m not sure I follow. I came up with 8 and I can’t seem to understand how 15.

A ship leaves at noon (not every 12 hours) you would never catch the ships ahead or behind you and so there would only be the ships moving towards you. You leave at noon so you will see the ship arriving and one each day at noon for seven days to include the one about to leave at the destination is the eight. In order for the number to be 15 the puzzle should have read every 12 hours not noon. Am i wrong?

sebbie3000| Profile November 3rd, 2008 - 7:00 amI honestly don’t get it. I worked it out by drawing two lines, each with 7 marks on (to indicate the days). I drew a diagonal line from the first point on one line to the last point on the other line – this would be the journey you take. Now, because all ships are moving at exactly the same speed, I drew the journeys of the other ships as diagonal lines. As you are travelling the same speed as every other ship, you will never catch up with those in front of you until they return, the same for those behind you (they would never catch you until you turn back to leave). Therefore, none of these lines intersect.

However, when you draw in the return journeys, then you can count the intersections. It only makes twelve you see during your voyage (I’m not including the one that docks as you are about to leave, as it’s not seen ‘during the voyage’. I cannot understand the other explanations, as it is a linear journey, everything at the same speed, all variables the same (an assumption, as nothing else is specified), and the wording (‘meet’ and ‘during your voyage’

suineg| PUZZLE MASTER | Profile November 3rd, 2008 - 10:24 amLet me try to explain myself better:

grimdeathwh: When you depart there are already ships getting back to Southhampton that is your starting point, a ships departs every day at noon if that so and the ships are in opossite directions (Southhamptom-New York vs New York- Southhampton, your ship is going to meet a ship every 12 hours because they are in opossite directions, more over the ships that are in the same directions of you in the trip, turn back at some point of your trip as the speed is constant, the 12 hour interval between each crossing remains for the whole trip.

Sebbie3000: I hope that with my explanation above it clarify a little bit the crossing part, and as the ship is docking in your harbor while you are departing, you pass by the ship during your voyage also when you are arriving the other harbor(New York) you meet the other boat while arriving.

Cool see ya.