# Mind challange when friends buys a car

• Grinder

#### Grinder

Four friends A, B, C and D are buying a car together.
They agree that everyone should have one of the first four trips all alone.

But the following conditions apply:

1. If D is allowed to get on the first trip, C would have the third trip.

2. If A or D take the second trip, C would have the first trip.

3. If and only if A receives the third trip, B want to have the second trip.

4. Will D get the third trip, A wants the second trip.

5. Will D get the last trip would C have the third and A the first.

In what possible orders can they take the first four trips so that all is happy?

Good luck,folks! =)

Welcome to PF, Grinder!

CABD, CDAB, or CDBA

Thanks!

You have to justify the thought. Are there more? ;)

/Grinder

CABD, CDAB, or CDBA

Justification is an exhaustive search of all possibilities

Justification is an exhaustive search of all possibilities

Oops! I mistyped my first solution and miss checked my second solution.

Thanks!

You have to justify the thought. Are there more? ;)

/Grinder

No, there are no more:

It is easiest to verify the possibilities for D.
If D is first, the rules dictate uniquely when the others go, leading to a contradiction.
With D second, the order has to be CDBA.
Finally with D 4th, we get another contradiction.

Hi!

What about ACDB and BCDA then?

What conditions are they violate? Or do they satisfy all conditions??

/Grinder

and yes...I found the smilie button!

Hi!

What about ACDB and BCDA then?

What conditions are they violate? Or do they satisfy all conditions??

/Grinder

and yes...I found the smilie button!

"4. Will D get the third trip, A wants the second trip."

every one is wrong here... i will tell you how...

go back read the question again and solve it...

ACDB and BCDA is wrong

It is easiest to verify the possibilities for D. but If D is first, the rules dictate uniquely when the others go, leading to a wrong answer.With D the order D has to be CDBA.With D third, CADB follows.Finally with D fourth, we get another wrong answer.

Hi everyone,

Unless I am misreading the question, the answer is ABCD. To me the list of conditions is just that a list. IF this one does this than that one will be satisfied if he does this. In that case the only condition that has everyone happy in the end is condition 5 If D is last then C wants to be third and A wants to be first. That leaves B to be second.