prisoner two doors with lady and tiger
A prisoner is faced with a decision where he must open one of two doors. Behind each door is either a lady or a tiger. They may be both tigers, both ladies or one of each.
If the prisoner opens a door to find a lady he will marry her and if he opens a door to find a tiger he will be eaten alive. Of course, the prisoner would prefer to be married than eaten alive :).
Each of the doors has a statement written on it. The statement on door one says, “In this room there is a lady, and in the other room there is a tiger.”
The statement on door two says, “In one of these rooms there is a lady, and in one of these rooms there is a tiger.”
The prisoner is informed that one of the statements is true and one is false.
Which door should the Prisoner open?
See Solution
Prisoner should open door number 2.
How?
Lets assume statement on the first door is true then second statement will also be true(as there will be a lady in one door and a tiger in other door), but as we already know that only one statement can be true, so first statement can not be true.
Now if first statement is false, it implies these possible scenarios
| Door 1 | Door 2 |
|---|---|
| Tiger | Tiger |
| Lady | Lady |
| Tiger | Lady |
But as second statement is true, so it means behind one of the door there is a lady and in other door there is a tiger so options with both lady and both tigers are ruled out and only third option remains valid, thus the prisoner should choose door number 2.
if first is true second would necessarily be true . so not passible ,therefore first is false and 2nd is true so 2nd door is the correct answer
My explanation is different … I took the statement “The prisoner is informed that one of the statements is true and one is false” into consideration … one of the statement means the statement containing the “one of” is true which is second statement and if second statement is true obviously the first statement should be false … so if first statement is false then there should be tiger in the door one and conversely there should be a girl in the second door … so opening door number 2 is correct according to logic ..
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I also thought similarly, but the given solution has no ‘Loop hole’…
‘Loop hole’ in your solution is [Which was mine too]…:
the description says… both could be tiger and both could be girl… so we can’t say for sure that second is correct – all by it self…