The cake is a liar! Part 3

We note that all the statements were "It wasn't so-and-so." Therefore, if it was Alan who ate the cake. Then the false statement was "It wasn't Alan." And there were only $3$ such statements, therefore, it wasn't Alan who ate the cake. The numbers of "It-wasn't" statements of the six persons are given below. Only Chris has $4$ such statement, hence it was $\boxed{\text{Chris}}$ who ate the cake.

Since 4 people are telling 1 lie , we just have to find the person whose name comes in exactly $4$ person's statements. {Since all the statements are 'wasn't' type}

=> The answer is $\text{Chris}$

BTW @Jack Smith nice problems. I have tried all four.

Chris was the only name mentioned 4 times; that was the 4 lies!

All of them were defending 3 other friends. We're told that 4 of the defensive statements are false, then we just need to count how many defense each of them received from their friends. If any had exactly 4, then they must be the guilty party.

Alan = 3 (by B, D & F)
Ben = 2 (by A & C)
Chris = 4 (by B, D, E & F)
Dave = 3 (by A, E & F)
Emma = 3 (by A, B & C)
Frank = 3 (by C, D & E)

Answer = Chris

All the statements are "Wasn't"s. Which makes it easy.

And there are 4 people telling ONE LIE. Which means, there's this one little slippery statement, that 4 people are making.

Just look for 4 similar statements, and you get: "It wasn't Chris." being said by 4 different people.

That's the lie. Oh Chris, you naughty cake lover <3