Monty Hall

[echoes]

Funny how the problem seems so much simpler when the river and bridges are replaced with an aeroplane and 2 landmarks.

Does it? As I said, as far as I am concerned, the concept is essentially the same with any 'moving substrate' - I think I mentioned rivers, conveyor belts, escaltors and trains - but we can, indeed, add air (and plenty of other things) to that list as well However, the principle is the same for all of them.

Kind Regards, John

It is of course, but until one realises that [the moving substrate], it's not easy to think of the river water as the substrate against which the man is rowing rather than the land with the bridges.

 

[JohnW2]

It is of course, but until one realises that [the moving substrate], it's not easy to think of the river water as the substrate against which the man is rowing rather than the land with the bridges.

That's obviously true - and is the 'mistake' ('making work for themselves') which most people make when they first encounter the river problem. However, contrary to what you suggested, I would personally have thought that the corresponding difficulty would be even greater with an aircraft, because the 'substrate against which it was flying' (the air) cannot even be seen to be moving in the way that a river usually can! I guess our minds must work differently!

Kind Regards, John

 

[ban-all-sheds]

It is of course, but until one realises that [the moving substrate], it's not easy to think of the river water as the substrate against which the man is rowing rather than the land with the bridges.

He's not rowing against it - he's travelling on it.

 

[JohnW2]

He's not rowing against it - he's travelling on it.

Exactly - and if that doesn't count as 'a clue', I don't know what would I reckon that Mr Einstein might have something to say about the matter!

Kind Regards, John

 

[ebee]

So are we ready to agree the answer now that sufficient time has passed?

And , perhaps more importantly, how we arrived at the solution?

 

[EFLImpudence]

I'll admit I still haven't got it.

 

[JohnW2]

I'll admit I still haven't got it.

Do you want more time, or would you like 'all to be revealed'?

Kind Regards, John

 

[EFLImpudence]

Just as well give the answer.

I'm obviously missing something.
I am stumped by the ten minute reference and the two variable speeds.

 

[JohnW2]

Just as well give the answer.
I'm obviously missing something. I am stumped by the ten minute reference and the two variable speeds.

To start with, forget all about the shore, and just think about the movement of the rower relative to water. When the hat is lost, the hat just sits on theh water, and never moves relative to the water. The person rows away from the hat, at some speed relative to the water, for 10 minutes. He then turns and rows back towards the hat, rowing at the same speed relative to the water as before. He therefore must take 10 minutes to get back to the hat.

Total time from losing hat to being reunited with it is therefore 20 minutes. Now think of the shore again. The river (and hat) travel the 1 mile between bridges between the time the hat was lost and the rower being reunited with it. The river (and hat) therefore moved 1 mile (relative two the shore in 20 minutes - aka 3mph.

As they say. Simples

As has been said, this same concept is also seen in relation to conveyor belts, escalators and anything else where someone/something is moving relative to a moving substrate. There are hundreds of variants of this 'puzzle' out there, plus a good few real-world applications.

Kind Rehards, John

 

[ban-all-sheds]

Just as well give the answer.

I'm obviously missing something.
I am stumped by the ten minute reference and the two variable speeds.

You are on one of those travelators at an airport. If you put down your bag, and walk away from it for 10 seconds, then turn around and walk back to it, how long does it take you to get back to it, assuming you walk no faster or slower than you did before?

 

[EFLImpudence]

D'oh.

So, we don't know and cannot determine - and it doesn't matter or make a difference - how fast he was rowing.

Some paper wasted.

 

[ebee]

I must admit it took me a while thinking about river minus boat speed for 10 mins then river plus boat speed for that distance he travelled in the ten mins plus another one mile too.

Until I got the Eureka moment and realised what John just said and then realised that his speed (on river not viewed from shore) was irrelevant providing that it was constant throughout the whole trip.

Phew. it foxed me until it clicked.

Know as a "kickself moment"

 

[JohnW2]

Note that it is essential that the question says that the rower passed the first bridge and then rowed as far as the second bridge.

If that wasn't stated, people might try applying the "if the question has been asked, there must be a unique answer, regardles of the speed of rowing" approach that was used in the simple solution of the 'hole through sphere' problem. They would then (by analogy with the 'hole in sphere') look at the case in which the speed or rowing relative to water was zero, and get into all sorts of trouble!

By stating that the rower passes both bridges, rowing speed relative to water was clearly greater than zero, hence invalidating the above approach - since there is at least one rowing speed (zero) for which the answer is not the same! (and thereby indicating that one has to be very careful before applying the "there must be a single answer" approach!).

Kind Regards, John

 

[JohnW2]

D'oh. So, we don't know and cannot determine - and it doesn't matter or make a difference - how fast he was rowing.

Exactly - provided that, as I've written, the speed of rowing is not the same as the speed of the river (but, as I've said, the wording of the problem precludes that, since rower managed to get the 1 mile from bridge 1 to bridge 2),

Kind Regards, John

 

[JohnW2]

D'oh. ... So, we don't know and cannot determine - and it doesn't matter or make a difference - how fast he was rowing. ... Some paper wasted.

Actually, the 'plodding' algebraic approach only requires one small piece of paper:

Untitled

• JohnW2
• 29 Sep 2013
• 1

Although it detracts from the 'puzzle, nature of the exercise, the 'advantage' of the algebraic approach is that it could be easily adapted to more complicated variants of the problem (e.g. changing rowing speed etc.) in a way that would often be difficult or impossible with the 'easy' approach.

Kind Regards, John