Math Is Fun Forum

Well you are on the right way, but guards can only answer Yes or No, so the prisoner will have to ask different question.

Yeah, but he told them that the last horse wins. I have already stated that the point of puzzle is to make you think in another way.

You have a system of 3 equations here:
From the first one find x, it is
x=6-y-z
put it in the second one:
2(6-y-z)-3y+4z=4
12-2y-2z-3y+4z=4
-5y=-8-2z   /*(-1)
5y=8+2z
y=(8+2z)/5
Now put x, y in the third one:
6-(8+2z)/5-z+(16+4z)/5-z=6
6+(8+2z)/5-2z=6 
(8+2z)/5=2z         /*5
8z=8
z=1
than:y=(8+2)/5=2
and:x=6-2-1=3
There are some other ways to do it- shorter ones :). If you are interested, I can show you.

yep, that's it.

A very interesting idea. I like it.
The actual solution is:
Let's say that sons are:A, B, C  where A has X, B has Y and C has Z (X,Y,Z - horses)
If the king orders A to rides C's horse, B to ride A's horse and C to ride B's, they would all try to make the horse they are riding at the moment, come first.(because if A rides Z, it isn't his horse and he doesn't want it to come last- he wouldn't get the property in that way).
That's it.

No, the solution is not morbid at all.
I should have emphasised that one of the sons will get the property only if their horse is the last. This should help.

Nope. Sons have three horses. 3 sons- have 3 horses, 1 son - has 1 horse.

Then sons wouldn't be involved in race (actively).

Sons have to ride the horses.

I was not precise enough. He told them that the last one would have all of his property.

Wow, a very long one - but correct. Yes, there is a shorter solution for this:
As we have distance which is cut by two straight lines on the one that we need to find equation for we will do this:
d(A,L2)-distance between L1: y1=2x1+5 and L2: y2=2x1+10, where A is point that belongs to L1-(we will pick a number for y, let it be 1, and then we find value for x, which is -2):
so A(-2,1)
d(A,L2)= |mx1-y2+n|/sqr m^2+1 ; x1= -2;y2= 1
d(A,L2)=sqr5
*Now triangle can be formed(right angled)- draw it. we have sqr10 and sqr5
c^2=a^2+b^2; c=sqr10 and a=sqr5
then b=sqr5
Now as a=b=sqr5 it means that triangle's angles are 90, 45, 45.(if this was not the case we would solve it using trigonometry)
As we have formula:
tanß=|(m2-m)/1+m*m2|  where ß=45 is angle between two lines; m2=2,  m- unknown
find m from here and you will get
m'= -3 ; L' : y'=-3x'
m''=1/3;  L'' : y''=1/3x''

Yes, that is obvious, so than it wouldn't be a puzzle- or at least not a good one. I remember that I have been working on similar or maybe the same puzzle before so that's why I suggested this solution. I would like administrator's comment on this, if possible.