## Mind challange when friends buys a car

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!! =)
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 Recognitions: Homework Help Welcome to PF, Grinder! Spoiler CABD, CDAB, or CDBA
 Thanks!! You have to justify the thought. Are there more? ;) /Grinder

Mentor

## Mind challange when friends buys a car

 Quote by I like Serena Spoiler CABD, CDAB, or CDBA
Spoiler

Justification is an exhaustive search of all possibilities

Recognitions:
Homework Help
Oops! I mistyped my first solution and miss checked my second solution.

 Quote by Grinder Thanks!! You have to justify the thought. Are there more? ;) /Grinder
No, there are no more:

Spoiler
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!!

Recognitions:
Homework Help
 Quote by Grinder 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. Did I misread the question?