A Missing Key

Logic Level 2

Clarification : Only one of these 3 boxes has the key.

Box 1 Box 2 Box 3 Not enough information

View wiki
Calvin Lin by Calvin Lin

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Chew-Seong Cheong
Mar 24, 2016

Considering all the three cases of which box the key is in, we get the following truth table.

If the key is in The key is in Box 1. The key is in not Box 1. The key is in Box 3. Box 1 T r u e F a l s e F a l s e Box 2 F a l s e T r u e F a l s e Box 3 F a l s e T r u e T r u e \begin{array} {cccc} \text{If the key is in} & \text{The key is in Box 1.} & \text{The key is in not Box 1.} & \text{The key is in Box 3.} \\ \hline \text{Box 1} & \color{#3D99F6}{True} & \color{#D61F06}{False} & \color{#D61F06}{False} \\ \text{Box 2} & \color{#D61F06}{False} & \color{#3D99F6}{True} & \color{#D61F06}{False} \\ \text{Box 3} & \color{#D61F06}{False} & \color{#3D99F6}{True} & \color{#3D99F6}{True} \end{array}

There are two cases where exactly two statements are false, therefore, we have not enough information \boxed{\text{not enough information}} to solve the problem.

10 Helpful 1 Interesting 2 Brilliant 1 Confused

Anyway the first and second statements on Box 1 and Box 2 are negation so either of that is false. Both can not be false at a time. So third statement is always false since Exactly two statements are false. hence the possibility is in Box 1 only.

Srinivas Nani - 5 years, 1 month ago

but if the key is in box 3, then the third statement is true as well as the second, because it is not in box 1.....

Joshua Henry - 5 years, 1 month ago

Key is in Box one. If the key was in box 3, the 2nd statement would be true.

Myra Guidi - 6 months ago

Either the first or the second statement is true as they both are negations of each other.

Examining both the cases, we see that the other two statements are false when either of them is correct and we get the possibilities that the key is located on either Box 1 or Box 3.

Hence there is not enough information to determine where the key is located.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Christopher Unrau
Apr 22, 2016

Simply by using trial and error, we can find all possible solutions. I'll label the three statements a, b, and c sequentially. If a is true, b and c are false. However, if b is true, a and c are false. So we have more than one situation that fits criteria, and thus don't have enough information.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Calvin Lin , this is rubbish ! What do you mean not enough information ? !!
Let me show you that there is. The problem clearly states that exactly 2 of the statements are false.

Case 1 : If we assume that the keys are in box one, then statements number 2 and 3 become automatically false. And this satisfies the conditions of the problem.

Case 2 : If we assume that the keys are in box 2, then statements 2 and 3 certainly become possible, so we cannot conclude that there are exactly 2 false statements. So we dismiss it.

Case 3 : If we assume that the keys are in box 3, then statements 2 is certainly still possible. And the reason is that statement number 2 simply says that the keys are not in number 1 So we cannot conclude that there are exactly 2 false statements. So we dismiss it.

And the fact is that even though there is the possibility that the keys are in box number 2, the problem did not ask for logical Necessity ! And THERE IS ENOUGH INFORMATION TO CONCLUDE THAT THE KEYS THE KEYS ARE IN BOX NUMBER 1 !!.

DarkMind S. - 4 years, 11 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...