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## 4 Facts and 4 Ladies

Posted by trickofmind on June 11, 2010 – 8:29 am

If you are feeling very confident on logic here is a bit of challenge:

Here are 4 facts about 4 ladies:
(a) Rosie earns more than Miss Christy, who lives exactly six miles from Ivy, who lives directly south of Miss Sayers;
(b) Olive earns more than the research chemist, who lives directly east of Ivy;
(c) The archaeologist earns more than Miss James, and Hazel earns more than the market analyst;
(d) The research chemist lives directly north of Miss Marsh, who lives exactly ten miles from Rosie, who lives exactly four miles from the optician. Which lady earns the most? Which lady is the market analyst? How far apart do Hazel and Olive live?

This post is under “MathsChallenge” and has 7 respond so far.
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1. 1. John24 Said：

Which lady earns the most? Hazel
Which lady is the market analyst? Olive
How far apart do Hazel and Olive live? 8 miles

2. 2. John24 Said：

Which lady earns the most? Hazel
Which lady is the market analyst? Olive
How far apart do Hazel and Olive live? 4 miles

3. 3. Karys Said：

That’s a tough one

I noticed that when two ppl are mentioned in the same sentence with their job, name or first name, they are different. Moreover, in any sentence the two mentionned women are mentionned according to different caracs.

4. 4. Karys Said：

I FOUND THAT ONE

That was something ^^

As I said, if two people appear in the same sentence (actually, the word shouldn’t be sentence, but you should have understood…) they can’t be the same.

I constructed 3 “matrices” Surname/Foren.(1), Sur/Job (2), Job/Foren. (3), respecting these orders : (see initials) RIOH (forenames), MG/MS/MJ/MM (surnames), rc/ma/a(r)/opt (quite irregular…) (jobs).

Something like that, numbers positioning the matrices :

R : 1 1 1 1 . 2 2 2 2
I : 1 1 1 1 . 2 2 2 2
O : 1 1 1 1 . 2 2 2 2
H : 1 1 1 1 . 2 2 2 2
. : . . . .
r : 3 3 3 3
m : 3 3 3 3
a : 3 3 3 3
o : 3 3 3 3

See…I highly recommand you to write down the matrices on your own so that you understand better how my thinking works… That will be ugly, since I don’t want to have 30 matrices to show each step one by one.

Each matrice element will be marked “0″ when we know that the corresponding traits are not related to the same person, “x” when we do not know, and 1 when 3 “0″s are on the same column or line already (that means we are sure they are the same because it cannot be differently)

Just using the sentences we get :
R : 0 x x 0 . x x x 0
I : 0 0 x x . 0 x x x
O : x x x x . 0 x x x
H : x x x x . x 0 x x
. : . . . .
r : x x x 0
m : x x x x
a : x x 0 x
o : x x x x

Now, we know that I is South from MS (a), and rc is East of I(b). I assume that if you say East, that’s East and not NE nor SE.
So MS/rc=0 (matrix 3)

Moreover, rc is North from MM : MM/I=0

R is 10m from MM, 4m from opt. MM/opt=0

R : 0 1 0 0 . x x x 0
I : 0 0 1 0 . 0 x x x
O : x 0 0 x . 0 x x x
H : x 0 0 x . x 0 x x
. : . . . .
r : x 0 x 0
m : x x x x
a : x x 0 x
o : x x x 0

there are 3 “0″s on matrix 1 ! you put a 1 on MJ/I, Ivy is Miss James. Miss James cannot be anybody else, complete with 0’s. that makes MS/R=1 !!!

then they share same relations with the “jobs”. MS=R, MS/rc=0 therefore, R/rc=0. THREE ZEROS !!! Do the same for Ivy…

R : 0 1 0 0 . 0 x x 0
I : 0 0 1 0 . 0 x 0 x
O : x 0 0 x . 0 x x x
H : x 0 0 x . 1 0 0 0
. : . . . .
r : 1 0 0 0
m : 0 x x x
a : 0 x 0 x
o : 0 x x 0

You now know who’s rc, Mrs Christy, and Hazel… Mrs Christy is Hazel.

R : 0 1 0 0 . 0 x x 0
I : 0 0 1 0 . 0 0 0 1
O : 0 0 0 1 . 0 x x 0
H : 1 0 0 0 . 1 0 0 0
. : . . . .
r : 1 0 0 0
m : 0 x 0 x
a : 0 x 0 x
o : 0 0 1 0

Now we know who’s who, but we do not know who’s market analyst or archeologist. Let’s replace all that we know with the forenames initials.

(a) R earns more than H, who lives exactly six miles from I, who lives directly south of R;
(b) O earns more than H, who lives directly east of I;
(c) The a earns more than I, and H earns more than the ma;
(d) H lives directly north of O, who lives exactly ten miles from R, who lives exactly four miles from I.

That’s much “cleaner”…

Now with the geographical positions.

from (a) and (b), we get something that shape :

R . *
.
.
I . H
. . .
. . .
. . O

(c) is still useless, but from (a) and (d) you have OR=10miles, IR=4m, IH=6m.
We assume there are right angles…
With these measures you have only one configuration left. We can calculate with Pythagoras theorem in R*O the distance *O, knowing R*=IH.

OH=4m.
How far apart do Hazel live apart from each other ? 4 miles.

The market analyst earns less than H, and that leaves only 1 possibility : Ivy is the market analyst.
And then I ask myself… wtf, Ivy is Optician already… That would mean someone is not working !!!

5. 5. Karys Said：

lol, the matrices look like you drank too much.

6. 6. Gary Holmes Said：

1) Karys:
Have u been drinking? Pls make sure u don’t drive? Don’t want u 2 get a DUI citation.

2) Karl:
Need clarification pls?
Was the “10 miles” Linear-Distance? or Road-Distance?

If it’s Road-Distance, then 4 mi + 6 mi = 10 mi: easy solution.

However, If it’s Linear-Distance, then we’ve got a problem: When ‘a’ to ‘b’ is 4 mi, and ‘b’ to ‘c’ is 6 mi => ‘a’ to ‘c’ is x mi, since the distance is diagonal.

4 sq + 6 sq = x sq
x = sq root of (16 + 36) = sq rt of 52 = 7.2111 mi.

Gary Holmes

7. 7. Fat Guy Said：

That’s ten facts and three questions.

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