# Logic Problem – test your logic

1. Jul 10, 2004

### Tigers2B1

Here’s a tough logic problem –

Mr. And Ms. Astor, Mr. And Ms. Brice, and Mr. And Ms. Crane were seated around a round table – each of the married couples facing each other on opposite sides of the table.

At the table:

1. Exactly three people sat next to at least one murderer.
2. Exactly four people sat next to at least one extortionist.
3. Exactly five people sat next to at least one swindler.
4. Six people sat next to at least one thief.

Of the types of crimes:

5. No two types of crimes were committed by more than one person.
6. One person committed more types of crime than each of the other persons.

Of the people:

7. Mr. And Ms. Astor each committed exactly one type of crime, though not the same type.
8. Mr. And Ms. Brice were both swindlers.
9. Mr. And Ms. Crane were both thieves.
10. More women than men were swindlers.

QUESTION: Who committed more types of crimes than each of the other persons?

2. Jul 10, 2004

### Tigers2B1

HINT:
Make a seating arrangement with each of the couples sitting opposite from each other.

Create a diagram first showing all of the possible seating arrangements for murders. Then do the same, creating a separate seating diagram for the seating arrangements for extortionists, swindlers and thieves. Note the least number of murders, thieves, extortionists, and swindlers possible from the independent diagrams for each. Note the least number of crimes that will solve the problem - from looking at the diagrams.

3. Jul 10, 2004

### EFischer

Are the couples seated such that they alternate male and female around the table, or are the men on one side and the women on the other?

4. Jul 10, 2004

### Esran

Is it Ms. Crane?

5. Jul 10, 2004

### Tigers2B1

First - this problem is hard and you'd better get pencil and paper -

The men all sit on one "side" - directly opposite their wives. For example - if Mr. Brice sits between Mr. Crane and Mr. Astor than Ms. Brice would sit between Ms. Crane and Ms. Astor on the 'other side' of the table.

6. Jul 10, 2004

### Tigers2B1

SECOND HINT: NO.

7. Jul 10, 2004

### EFischer

Mrs. Brice, if the men are on one side and the women on the other. Mr. Brice if the men and women alternate.

8. Jul 10, 2004

### Parth Dave

Is it Mr. Crane?

9. Nov 22, 2004

### 0TheSwerve0

Ms. Brice, which should be Mrs. right?

10. Sep 9, 2005

### Orangejuice

oh man this thread is from a year ago, anyways how do you find these?
3. Exactly five people sat next to at least one swindler.
4. Six people sat next to at least one thief.

so isnt mr. & mrs brice & mrs. astor possibly the 3 swindlers?

im not sure but if two swindlers sit together doesnt it count as 4 people sitting next to swindlers?

11. Sep 10, 2005

### AKG

Ms. Astor was a swindler.
Ms. Brice committed three crimes, more than any other person: swindling, extortion, and murder.
Ms. Crane was a thief and an extortionist.
Mr. Astor committed theft.
Mr. Brice was a thief and a swindler.
Mr. Crane committed murder and theft.

12. Sep 10, 2005

### PhilosophyofPhysics

Hmm... I got Ms. Brice as the one committing the most types of crimes. I also wondered if there was enough information here. Did the three males all sit next to each other? Did they alternate between male and female? Can we find many answers?

Did I miss any requirments?

Mr. Astor: Thief, Murderer
Mr. Brice: Swindler, Thief
Mr. Crane: Thief
Ms. Astor: Swindler
Ms. Brice: Swindler, Extortionist, Murderer
Ms. Crane: Thief, Extortionist

13. Sep 10, 2005

### PhilosophyofPhysics

here's another with Ms. Crane as committing the most types . You can see what went wrong here as well

Mr. Astor: Thief
Mr. Brice: Swindler, Thief
Mr. Crane: Thief
Ms. Astor: Swindler, Murderer
Ms. Brice: Swindler, Extortionist
Ms. Crane: Thief, Extortionist, Murderer

14. Sep 10, 2005

### AKG

PhilosophyofPhysics, both your answers are wrong as they contradict clue 7. In both your answers, you have an Astor committing two crimes, but the clue says that each Astor committed only one crime. However, you may be right that there are different possible answers if the people are arranged on the table differently, I'll think about that.

15. Sep 10, 2005

### PhilosophyofPhysics

Oh, I see. I just focused on them committing different types of crimes.

16. Dec 21, 2005

### davee123

Ressurrecting this thread for the 2nd time:

Given the problem as initially stated, there are four possible solutions:

Mr. Astor: Thief
Mr. Brice: Thief, Swindler
Mr. Crane: Thief, Murderer
Mrs. Astor: Swindler
Mrs. Brice: Swindler, Extortionist, Murderer
Mrs. Crane: Thief, Extortionist

Mr. Astor: Thief
Mr. Crane: Thief, Extortionist
Mr. Brice: Swindler, Extortionist, Murderer
Mrs. Astor: Swindler
Mrs. Crane: Thief, Murderer
Mrs. Brice: Thief, Swindler

Mr. Brice: Thief, Swindler
Mr. Astor: Thief
Mr. Crane: Thief, Extortionist
Mrs. Brice: Swindler, Extortionist, Murderer
Mrs. Astor: Swindler
Mrs. Crane: Thief, Murderer

Mr. Astor: Thief
Mrs. Brice: Thief, Swindler
Mr. Crane: Thief, Murderer
Mrs. Astor: Swindler
Mr. Brice: Swindler, Extortionist, Murderer
Mrs. Crane: Thief, Extortionist

The arrangement of crimes is always the same (rotated or mirrored). And invariably Mr. Astor is just a thief, and Mrs. Astor is just a Swindler. The remaining four switch around a little. Hence, to get a singular solution from the initial problem (without the hint that men and women are seated together), one must stipulate something else. So, say:

11) the two wives that are thieves do not sit exactly 1 seat apart.

or:

11) Mrs. Astor sits next to 2 men

or:

11) Mr. Brice committed fewer crimes than his wife and sits next to at least 1 of the wives.

etc.

DaveE

17. Jan 5, 2010

### little.holmes

Here's what I got:

Mrs. Astor: Swindler
Mr. Aster: Thief
Mrs. Crane: Murderer, Thief
Mr. Crane: Thief, Extortionist
Mrs. Brice: Swindler, Thief
Mr. Brice: Swindler, Extortionist, Murderer

Thus Mr. Brice is the answer.

18. Jan 8, 2010

### ƒ(x)

Do you mean that one and only one person committed more than one type of crime (Ex. Mr A is a thief and a murderer while the others were each 1 type)? If that's the case, then you can't have 3 people sitting next to a murderer (you need two murderers side by side) and either your clue is wrong or two people can commit more than one type. For now, I will suppose that he or she can commit two types.

I don't know if this question has already been asked. I am reluctant to read through the rest of the replies because I have never seen this logic puzzle before and do not want to ruin it.

19. Jan 8, 2010

### little.holmes

No it only means that one person commited more crimes than the others so you cannot have 2 persons being the answer at a given situation.

And good luck for solving the puzzle, it is a very nice problem, though not as hard as it sounds once you draw the diagram and work one hint at a time. :)

Last edited: Jan 8, 2010
20. Jan 8, 2010