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The Six Doors

Puzzle:

You are in a room that has six doors. You must pass through all six doors, each door once only, in the correct order. Three are entrances only and three are exits only. Door A must be followed by door B or E; D by A or F; B by C or E; C by D or F; E by B or D; and F by C or D. Also A, F are entrance and B is exit. In what order you must pass through the doors?


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Solution:

The order is CFDABE.

Doors A, F are entrance and B is exit. We must alternate exits and entrances. Let the unknown entrance be X. With a "_" denoting an exit door the possible orders are:

(a) _A_F_X ; (b) _F_A_X ; (c) _X_A_F ; (d) _X_F_A ; (e) _A_X_F ; (f) _F_X_A
Neither (a) nor (c) are possible since A is followed by B or E and neither leads to F. Since A can only be preceded by D, (e) and (f) are possible as DA_X_F and _F_XDA, respectively. With D used, door F can only be preceded by C to give DA_XCF and CF_XDA, respectively. Door B must occupy the remaining space in each possibility (third door is exit) so X=E but C cannot follow E in the former and for the latter, B cannot follow F. This eliminates (e) and (f). Since only D precedes A, (b) is possible as _FDA_X and (d) as _X_FDA. For (d), the exit B must occupy a "_" but cannot be followed by F, and if it is the first door, neither the C or E that must follow as X can be followed by the remaining E or C, respectively. This only leaves (b) and only C (of the possible B,C,E) can precede F as CFDA_X and B must occupy the final "_" as an exit leaving E=X. Notice that the condition that E is followed by B or D cannot be satisfied.



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14 comments:

Odile S said...

It was less difficult than I thought. Am I supposed to leave my solution here?
I'll hide it at my blog instead.

nidhi said...

i think order is........
a-e-d-f-c-b

varun said...

ABEDFC

Anonymous said...

My order is f-c-d-a-b-e ..

~ Shireen

Anonymous said...

Entrances : A, E, F
Exits : B, C, D

Order of entry and exits: A, B, E, D, F, C

rahul said...

order is a->e->b->c->d->f

kishore said...
This comment has been removed by the author.
vivek said...

i think it is -- --
A-B-C-D-F-E

Karthik said...

ABEDFC... Sure

madhur said...
This comment has been removed by the author.
madhur said...

I donno whether you guyz even understood the puzzle properly or not

These 3 conditions must be followed with out any expecption
A -> B, B -> E, C -> F

This 3 conditions you would get easily from the given condtions simply by applying elimination rule.

Solution for this puzzle would be
C -> F -> D-> A -> B -> E

last (karthik's) solution is also correct (ABEDFC) if you start from exit.

but all other solutions are wrong for sure

aditya said...

I think the ans should be
A B E D F C

aditya said...

the other solution which will result when the person is in the room already (mentioned in the question also) is :

C F D A B E

KAIFI said...

ya
the solution was quite tricky
the answer is
c-f-d-a-b-e