@Markiyan Hirnyk I think @Carl Love used GlobalSearch for reason. For instance, changing the population of A from 5 to 8:  DirectSearch:-GlobalSearch gives three (x,y) solutions whereas DirectSearch:-Search only gives one.

@Carl Love thanks for solution. and Markiyan Hirnyk

Do you know a formula to extract the x component from an expression,

e.g. some_maple_formula(Obj,x)=5*abs(x-3)+2*abs(x-6)+2*abs(x-5)+abs(x-1)+3*abs(x-7)  ?

Rouben Rostamian I knew about Euclidean distance formula but not the one which permits horizontal and vertical movement. I won't post homework problems because my student days are well behind me.

@Rouben Rostamian    Thx. But where did V^2 = v^2 + v^2*t^2*b'(t)^2 spring from? It looks a lot like motion equation  v^2 = u^2 + 2.a.s.  Also would you mind posting the code for the animation Pls

@Carl Love 

@Carl Love thx for your efforts. 

i tried to use the above code to model 3 dancers, 4 m apart. the ode plot didnt and the arc length might be wrong. could you fix it pls.

triangle_persuit.mw

@Carl Love and Kitonum for your solutions.

thanks also to ThomasRichard and @Carl Love for supportive comments regarding my questions on mapleprimes.

@tomleslie i concur with you. It doesn't seem in the "spirit" of the problem to do it like he did. He made a right angle cut to the small cheese OD, withdrew the knife and then another hemispherical cut. Then withdrew the knife and made another cut ( that's 3 cuts, not 1).

@tomleslie your solution got me thinking of an alternative way. I don't remember aall of those geometry formulas, but with integration, I only need to know the equation of a circle.

x^2+y^2=(16/2)^2;
yeq:=solve(%,y)[1];
#total area:
2*int(yeq,x=-8..8)=Pi*(16^2)/4;
#checks. Let D be the coordinate the cut has to make to remove 14Pi from the medium cheese.
2*int(yeq,x=D..8)=14*Pi;
fsolve(%);
#make the cut at coordinate of D [3.6671,0]
area of segment check:
2*int(yeq,x=%..8)=evalf(14*Pi);

BUT the solution on "School of Hard Sums", which doesn't require any fancy pants geomery or calculus, is found by placing the small cheese in the centre of the medium cheese and cutting a semicircular arc around it.
This C section is put with the small cheese=1 portion.

#Area of an annulus + area small cheese:
Pi*1/4*((16^2-12^2)/2+12^2);
50 Pi

@Thomas Richard 

Windows was indeed treating it as a text file. I removed the extension and success! Thx for your help.

I'm running win 7 BTW

@Thomas Richard thx for your input.

i removed the ini's from Maple18/win.bin, lib and Users.

i changed my text file to this:

interface(prompt=""):
e:=exp(1);
Digits:=15;
print("maple init loaded...");

And placed in  C:\Users\<my_account_mame>

Rebooted Maple and no result.

tried putting it into Maple18/win.bin, lib and Users (one at a time) -> same same

@tomleslie thx Tom.

Sorry i was not more succinct. I meant DirectSearch package.

I did state i was using M18.

You gave me the clue, I did a search on the MP website for " hdb" and saw what i'd known i'd seen b4, 

http://www.mapleprimes.com/posts/200289-Convert-Help-Of-Older-Maple-Version-To-18

@Carl Love it's a pity Maple doesn't have a Mathematica-esq "scan for issues" command.

@tomleslie and Kitonum. so logical.

Unfrortunately, Tom , when I run your code I get "Error, invalid input, expects 2 arguments, but received 1" .

in Maple 18....

@Carl Love thanks

@bfathi .sav are file extensions used by SPSS aern't they?