Liars Quiz Puzzle Answer

Five girls sat a test at University and, fed up with their parents' constant questioning about results, they devised a little scheme. Each girl emailed home two statements, one of which was true and the other false. This meant that the five sets of parents could, if they colluded with each other, work out the girls' positions in the test.

Which might prove to be harder than the test!

The girls' emails were:

Anne: I finished second and Debs was only fourth.

Beth: Anne was second but I was only third.

Cath: I came third and poor Emma was last.

Debs: I was fourth and Beth came top.

Emma: Luckily I came top and Cath was second.

Given the information received by the parents received can you determine the actual finishing order of the five girls.

There are a few ways into this puzzle, and here is one.

Two girls say that Debs is fourth. If this is not true then Anne was second  and Beth first. But if Beth is top then Emma's first statement is false and her second statement is true making Cath second. Anne and Cath can't both be second so Debs must be fourth.

As Debs is fourth Anne can't be second and from Beth's statement Beth must be third.

If Beth was third then Cath wasn't third and Emma must be last.

And if Emma was last her statement about Cath must be true, so Cath can second.

This just leaves Anne, who must have been top.

The full order is

  1. Anne
  2. Cath
  3. Beth
  4. Debs
  5. Emma


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