# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #1 Re: Puzzles and Games » Roman Numeral Puzzle ;) » 2005-06-23 09:28:05

Let's try putting V in the middle:
IVX = 10-(5-1)=6
?

## #2 Re: Puzzles and Games » What should be the question? » 2005-06-23 04:41:00

Zach wrote:

He asks any guard, "If I were to ask the other guard, which door I would have to go through to go to freedom, which one would he say?" Then, you take the opposite.

The truth telling guard will tell you that the other will say the door to doom (Say, the left), while the lying one would tell you that the truth telling guard will tell you that he would tell him it's the left door, as he's lying about what the TTG is going to say.

Simple!

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

,yep.

## #4 Re: Puzzles and Games » Horse race » 2005-05-31 09:16:20

cool_me wrote:

i guess the king wont tell them tht the property will be given to the person who loses or wins.he just keeps a race and then whoever loses the race will be the owner of tht royal property,
if this is not the answer then u shud try it out first!

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.

## #5 Re: Help Me ! » Plotting Linear Equations with Three Variables » 2005-05-27 05:57:24

ups . My apologies

## #6 Re: Help Me ! » Plotting Linear Equations with Three Variables » 2005-05-26 23:41:45

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.

## #7 Re: Help Me ! » Problem » 2005-05-26 08:47:33

(8*3)-3^0+8^0=24
I know that 3^0 is not the same as 3, but it was said that we need to use 8,8,3,3 - and as you can see every of these numbers are used. I though of it logically, that's why i did it in this way. ????

yep, that's it.

## #9 Re: Puzzles and Games » Horse race » 2005-05-23 20:09:37

I've got one which could be interesting.
.    .    .
.    .    .
.    .    .
You are supposed to connect these dots with only 4 straight lines without lifting a pen from the paper, from the moment you put it on.
*Note - if you make a line and than go back over it, it counts as 2 lines.

## #10 Re: Puzzles and Games » Horse race » 2005-05-23 09:18:54

stewie wrote:

Put each horse on a seperate conveyor belt that crosses the finsh line.  The horses have to run against the conveyor belt to prevent crossing the finish line and eventually they'll get tired and have to cross.

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.

## #11 Re: Puzzles and Games » Horse race » 2005-05-22 09:18:15

stewie wrote:

just say its a race to see who gets his kingdom, but "forget" to metion last place gets it.  There simple.

No, it's not the point of puzzle. The point is to force you to think in another way. If point of race is changed(meaning that the last horse wins), then something else should be also changed. What?

## #12 Re: Puzzles and Games » Horse race » 2005-05-22 09:13:03

Zach wrote:

I'm expecting the answer is that they're forced to shoot the horse?

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.

## #13 Re: Puzzles and Games » Horse race » 2005-05-20 23:13:48

Roraborealis wrote:

I think I have the answer! Tell them that whoever wins the race gets the property!

:):)
Nice try. No it's not the solution.
But, it is very simple. King has to make them do something with horses.- it will be easier now, I think.

## #14 Re: Puzzles and Games » Horse race » 2005-05-20 23:08:14

MathsIsFun wrote:

Three Sons. Sons have three horses. Does that make nine horses?

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

## #15 Re: Puzzles and Games » Horse race » 2005-05-19 22:59:31

Roraborealis wrote:

Stick a carrot in front of each horse.

That's good but the sons would still be trying to slow down the horses - so it wouldn't be a fair race after all

## #16 Re: Puzzles and Games » Horse race » 2005-05-19 22:55:42

Roraborealis wrote:

Then, just attatch the sons to the horses with their hands tied up! But attach them so they won't fall off. Or make them ride blindfolded.

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

Ok

## #18 Re: Puzzles and Games » Horse race » 2005-05-19 17:00:12

Sons have to ride the horses.

## #19 Re: Puzzles and Games » What should be the question? » 2005-05-19 07:49:45

I would really like if someone tried to solve this puzzle. Zach?

## #20 Re: Puzzles and Games » Horse race » 2005-05-19 07:23:07

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

## #21 Puzzles and Games » Horse race » 2005-05-18 11:22:13

Milos
Replies: 98

King is dying. He has three sons. Sons have three horses. King has decided to organize a horse race and will give all of his property to the son whose horse is the last at the race. However, he wants race to be fair, meaning that he doesn't want sons to slow down their horses. What will he do?

## #22 Re: This is Cool » Analytic geometry » 2005-05-18 11:07:32

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''

## #23 This is Cool » Analytic geometry » 2005-05-16 09:07:33

Milos
Replies: 4

Find equation of a straight line which passes thought O point with coordinates (0,0) if it is cut by two straight lines with equations:
2x+5-y=0; 2x-y+10=0; and length of the part which is cut by these two straight lines is sqr10.

I think that this one is interesting. Try it.

## #24 Re: Puzzles and Games » Easy one » 2005-05-16 08:42:29

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.

## #25 Re: Puzzles and Games » Easy one » 2005-05-16 06:38:24

OK, I thought of something else. If books are placed very neatly on shelf side-by-side than this could be correct. Take three books and organize them as they do it in libraries(so we could read the title of a book)- vertically. Start counting from left to right(as we usually do). You will see that your first page is 1000th. That would mean that in 12 hours worm will chew from 1st page of the first book to 1000th page of the last. 4 covers + 1000 pages of the book in the middle.