Math Is Fun Forum

I will refer here to your original diagram (I guess you still have it).

I used to tell my students that, in general, finding how to solve a problem has two main directions, forwards and backwards.
To solve this exercise, walking backwards makes it a simple one.
   
Let us assume first that the full range (R) of the missile was used.
In this case, the warship had to be on the circle whose center is ‘Y’ and radius is (R).
If we draw this circle, it becomes clear that WX is the shortest distance from W to this circle.
Therefore, the mathematical solution of T=f(D,R,S1,S2,S3) could take advantage of Pythagoras theorem of the right triangle SWY.

One may think that it is not necessarily to use the full range of the missile, say (k*R) instead of (R), where 0<k<1.
The same reasoning above also applies in case (k*R). Only the radius of the circle becomes (k*R) instead of (R).
This means that T_new = f(D,k*R,S1,S2,S3). That is (R) is replaced with (k*R) in the final formula of (T).
And by analyzing the variation of the function (T_new) with the variable parameter (k), we will find out that T_new > T for all values of (k).

This may be applied in real life. But, as you know, the situation here is just a math exercise.

For instance, when I saw your first diagram, I thought you got quickly the right logical answer of the situation related to the 2 directions of W and the missile.
Unfortunately, you changed your mind

As we will see, proving that your first diagram is right, and it gives indeed the minimum time of the mission is somehow simple if one discovers how to start it.

I believe you can prove it, right?

Sorry for the confusion. I thought that the meaning of 'towards the side of the other ship' is totally different from "towards the other ship'.

Let us assume that the two parallel straights of S and W are drawn horizontally.
The ordinary ship, S, was on the northern line and the warship, W, was on the southern one. Both were moving from west to east.
At t=0, the captain would have to change the direction of his warship, W, towards north-east. The angle formed by the new direction (straight line) of W and the horizontal line could be called θ for example. In theory, the angle θ could be any value between 0 and 90 degrees but the captain had to decide its exact value to achieve the minimum time for his mission. The trajectory of the missile is also a straight line (between the position of the warship, W, when the missile was launched and the position of the other ship, S, when it was hit by the missile).

Please don't hesitate to notify me if I missed something to clarify about the exercise.

Kerim

But, thanks to your first good work and my reply to you, our friend Bob was able to notice. more easily. the second right answer.
So, I guess, if Bob presented his solution before you did, you will likely be the teacher by noticing the second option as he did.

Anyway, this situation may look like a humble example of the saying:
"But many that are first shall be last; and the last shall be first."
So, as possible, I try always to be the last

Hi Bob,

Yes, we are all still students in life, since learning/discovering has no limit.

But, here, only a teacher may notice that 'k' is given twice in (2) and (5), though presented in different forms.

Following the norm, a student expects here that the right answer is (or has to be) given once on the list. So, when he finds the right answer, he just checks (x) on the expression (2) or (5), the one he got at his last step. But, by doing this, he also says, though without his knowledge, that none of the remaining 4 expressions is equal to the right value of 'k' which is wrong.

Kerim

The way I, a realistic rational person, see it is that every neural network is created by the human's brain.
Therefore, these neural networks cannot be made cleverer than their human creators though some creators try their best to give the world the impression they are, at least in some fields (while in reality they are not). They are just advanced tools which speed up the world's progress for the good and bad as well.

Anyway, if it is possible someday to make something more intelligent than the human's brain then the human up-to-date profession in every field, not only of photographer, will disappear altogether

For instance, the profession of photographer has now a chance to achieve new things by the use of new advanced tools; things which were impossible to make/create in the past.

Just to give an idea about my nature, I respect always other's views and knowledge no matter if they sound right or wrong to me.
And when I contact others, I simply say what I know while I understand fully that they may have their good reasons not to accept everything I say/know.

hi mrpace,

I draw an 18x18 table on Excel. I filled its diagonal with 18 zeros.
I let its below part be a replica of its upper one, since (P1,P2) = (P2,P1) for example.

By filling the rows of upper cells with 8 one's for each player, I got the total of matches equal to 144 (8*18).
And to check that every player plays 8 matches, I summed the cells of each row/player (horizontally) and of each column/player (vertically). It was possible to let every sum be 8.

Kerim