UPSC Maths Problems Challenge : A Problem A Day! (Day 20)

Today's problem is not from any IAS examination question paper or from similar sampler question sets but such type of logic problems do come in Civil Service Examinations a lot and this question was something I found this morning in my e-mail from Brilliant,a website which I have been seriously practising sums from about six months and believe me,they are very interesting,even when you are not subscribed to the paid premium package.

This problem is based on pure logic (Say,don't you love to go through Game Theory?) and I loved my experience solving it though I had to think for quite a while.

Read on to find the solution.I am sure you are going to love this,too.

(Original Photograph Source)

Today's Problem(02/07/2015)

Question Credit : http://brilliant.org/

Alan, Ben, Chris, Dave and Emma are eating a big cake. After eating, there was one slice left, and they decided to leave it for Frank but someone ate it! Frank knows that each of these 5 people are each telling one truth and one lie:

Alan: It wasn't Emma. It was Ben. 
Ben: It wasn't Chris. It wasn't Emma. 
Chris: It was Emma. It wasn't Alan. 
Dave: It was Chris. It was Ben. 
Emma: It was Dave. It wasn't Alan.

Who ate the last slice of cake?

In case of logic problems,you have to look very carefully into what you are looking at.It must be a very careful observation to get it going.So firstly,if we consider that "It wasn't Emma" is false,then the truth becomes that it was Emma and the true statement is it was Ben as well but how can that be it?We already know that only one person ate the cake.So,the statement "It wasn't Emma" has to be true and that "It was Ben" is false.

Now that we have considered that "It wasn't Emma" is true (and with some good logic behind it),It was Ben is false.So,it wasn't Ben who ate the cake.

We have to consider that "It wasn't Chris" in the second statement is false as we have taken "It wasn't Emma" to be true.So,it was Chris is true.

Then in the third statement,"It was Emma" has to be false because we considered "It wasn't Emma" to be true.So,"It wasn't Alan" is true.

In the fourth statement,we find "It was Ben" is false because from the first statement,we already have that it was not Ben.So,"It was Chris" is true.

In the fifth statement,we have that "It wasn't Alan" is true (as derived from the third statement).So,it was Dave has to be false.Therefore,the truth is that it wasn't Dave.

So,the only statement that holds to be true is that Chris ate the cake.So,the answer is that Chris ate the last slice of cake.