# The color of the hair

Three women were having lunch- Melanie, Rebecca and Debbie.

Melanie is older than the woman with black hair, but younger than the book keeper. The computer operator is doctor's younger sister. Rebecca is younger than the brunette, and Debbie is older than the blonde.

What color is each women's hair and what is her profession$?$

First let's reformat the text into mathematical comparisons (based on age):

1. Melanie > black
2. Book keeper > Melanie
3. Doctor > Computer operator
4. Brunette > Rebecca
5. Debbie > blonde

From 1. and 5. we get:

Melanie and Debbie are the oldest two (they're both older than at least a person), so Rebeca is the youngest.

From 2. we get

Melanie is the second oldest (she is older than a person and younger than another). So Debbie > Melanie > Rebecca.
And Debbie is The book keeper (since she is the only one older than Melanie).

From 1. we get:

Rebecca is the black haired woman.

From 3. we get:

Melanie is the doctor and Rebecca is the computer operator.

From 5.

Melanie is the blonde and Debbie is the brunette.

Recap:

From youngest to oldest:

• Rebecca: black haired, computer operator.
• Melanie: blonde, doctor.
• Debbie: brunette, book keeper.
The professions seem demographically correct too. :)

I think this is it:

Rebecca = Black hair and Computer operator.
Melanie = Blonde doctor.
Debbie = Brunette and Book keeper

• But why do you think this is it? Answers without explanation are liable to be removed. Jan 18, 2018 at 21:37
• @Randal'Thor I posted my answer and would post my explanation later, but then I saw Ibrahim's answer, already with a similar explanation that I would post. I thought it wouldn't make sense to post the same explanation. Jan 18, 2018 at 21:45

Four statements are given:
1. The book keeper is older than Melanie who is older than the black haired one
2. The computer operator is the doctor's youngest sister, so he is younger than the doctor
3. The brunette one is older than rebecca
4. Debbie is older than the blonde one

So

We can get a lot of information out of every of these statements:
1. means:Melanie does not have black hair, Melanie is the 2nd oldest woman,the black haired one is the youngest woman
3. means: Rebecca doesnot have brunette hair
4. means: Debbie does not have blonde hair,Debbie is older than someone, but she can only be the oldest or the youngest woman (Melanie is the 2nd oldest), so she is the oldest one meaning that she also is the book keeper. Since Debbie is older than the blonde haired woman, Melanie can only be blonde haired, because the other woman (of which we now know that she is the black haired Rebecca) that is younger than Debbie is black haired.
2. means: We know that Debbie is the book keeper, and the computer operator is younger than the doctor, so Melanie has to be the doctor and Rebecca is the computer operator.

=>

Final solution:
Debbie: Brunette book keeper
Melanie: Blonde doctor
Rebecca: Black-haired computer operator

Here's how to solve any of these types of puzzles

# 1. Breakdown the details

1. Melanie is older than the woman with black hair,
2. but younger than the book keeper.
3. The computer operator is doctor's younger sister.
4. Rebecca is younger than the brunette,
5. and Debbie is older than the blonde.

# 2. Rewrite in short form with > and < as given

1. Melanie > black hair
2. Melanie < book keeper
3. Comp op < doctor (sister doesn't matter)
4. Rebecca < brunette
5. Debbie > blonde

# 3. Rearrange so that all > and < are pointing in the same direction

1. Black hair < melanie
2. Melanie < book keeper
3. Comp op < doctor
4. Rebecca < brunette
5. Blonde < debbie

# 4. Join any lines with the same items

1. Black hair < melanie < book keeper
2. Comp op < doctor
3. Rebecca < brunette
4. Blonde < debbie

# 5. Deduce details

Since Melanie is in between a job and hair, both the job and hair must be different people

Looking at hair first since we have most details with hair and their relation to people

First, what hair color can't each person have? What ever color is on their line.
So that means

1. Melanie - brunette or blonde
2. Rebecca - black or blonde
3. Debbie - black or brunette

Looking back at the clues in relation to hair

Rebecca has to be younger than someone with brunette hair
Debbie has to be older than someone with blonde hair
Melanie has to be older than someone with black hair but younger then someone with hair we do not know (and we know these people must be different)


So from that we can deduce everyone's relative age Rebecca is youngest, Debbie is oldest so

Rebecca < Melanie < Debbie


# 6. Plug the details back in where they fit

1. Black hair (Rebecca) < Melanie < book keeper (Debbie)
2. Comp op < doctor
3. Rebecca < brunette
4. Blonde < debbie

# 7. Repeat #5 & #6 until it is solved

Looking back at the hair deductions we made earlier we can easily deduce the rest of the hair colors (you could go back to comparing >'s but this is easier)

Step 1

1. Melanie - brunette or blonde
2. Rebecca - black or blonde
3. Debbie - black or brunette

Step 2

1. Melanie - brunette or blonde
2. Rebecca - black or blonde
3. Debbie - black or brunette

Step 3

1. Melanie - brunette or blonde
2. Rebecca - black or blonde
3. Debbie - black or brunette

Now plug all that in and we can work on the jobs

1. Black hair (Rebecca) < Melanie (blonde) < book keeper (Debbie)
2. Comp op < doctor
3. Rebecca < brunette (debbie)
4. Blonde (melanie) < debbie

We know the hair so we can get rid of it and just look at names and jobs

1. Rebecca < Melanie < book keeper (Debbie)
2. Comp op < doctor
3. Rebecca < debbie
4. melanie < debbie

And then join lines with the same names

1. Rebecca < Melanie < book keeper (Debbie)
2. Comp op < doctor

We already know debbie's job so

1. Rebecca < Melanie
2. Comp op < doctor

Therefore Rebecca must be the computer operator and Melanie is the doctor

# Conclusion

1. Melanie is a blonde doctor
2. Rebecca is a black-haired computer operator and Melanie's younger sister
3. Debbie is a brunette book keeper

My first time actually solving one of these. It is interesting to deduce the algorithm for making these puzzles from solving one. Fun!