The cake is a liar! Part 2

Let us assume who ate the cake one by one and check the number of statements that are true. For example, if Alan ate the cake, then the first statement of Alan was true and the second one is false; both statements of Ben were false; both the statements of Chris were true and so on. And doing the same with Ben, Chris, Dave and Emma. We assign a true statement with 1 and false one with 0, we get the following table.

From the table we see that only if $\boxed{\text{Emma}}$ ate the cake that we have exactly $5$ true statements.

Let us group some sentences [A-Alan, B-Ben, C-Chris, D-Dave, E-Emma]

Contradictory sentences (If one is right, the other in the pair is wrong):-

It wasn't A <=> It was A

It wasn't D<=> It was D x2 (there are 2 such sentences)

It wasn't C<=> It was C

Other sentences:-

It wasn't B x2 (there are 2 such sentences)

It wasn't E

Total=>10 sentences out of which only 5 are true.

If D was the culprit, we would have 7 true sentences.

If A or C was the culprit, we would have 6 true statements.

If B was the culprit, we would have 4 true statements.

The only assumption that'll satisfy the initial conditions is assuming E (Emma) was the culprit.

Everyone was defended by another friend (by the nots in their wasn't), including Ben who was defended twice by Alan and Chris. If Ben was guilty, then only 4 of those defensive statements are right and they would need a true accusation against him to make it to the fifth truths, but nobody did accuse Ben, lucky him.

If someone other than Ben was guilty, then 5 of those defensive statements are right and they would NOT need another true accusation against the guilty party to make it to the fifth truths. Amongst the other four, nobody did accuse Emma, so she must be the cake slice thief.

I'm only 13 but read that emma just said who it wasnt not who she thinks it is. I did no maths, I just had a logical guess!

There are so many "was"-es, yet only 1, or none of them, is true.

And "was" and "wasn't" statements for the same name, cannot fall under the same category. ("It wasn't Alan" and "It was Alan." cannot both be true.)

We have 4 "was" statements, and 6 "wasn't" statements. Most of the "was" statements would be false, because only 1 person ate the cake.

Let's start by assuming that all 4 "was" statements, are false. Which would mean "It wasn't Chris, Dave, nor Alan.". AND 1 of the remaining statements, is false.

We're left with Ben, Emma. If it was Ben, then, "It wasn't Ben" would be false. And here's the key, we have 2 "It wasn't Ben" statements.

But only ONE of the remaining statements, is false. Which means, Ben is not guilty.

And Emma, is the cake-eater.