A problem by British puzzlist Hubert Phillips:
In writing home about an examination, five schoolgirls each made one true statement and one untrue one. The relevant passages:
Betty: Kitty was second in the examination. I was only third.
Ethel: You’ll be glad to hear that I was top. Joan was second.
Joan: I was third, and poor old Ethel was bottom.
Kitty: I came out second. Mary was only fourth.
Mary: I was fourth. Top place was taken by Betty.
In what order did they place?
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- Kitty
- Joan
- Betty
- Mary
- Ethel
It’s possible to begin with any of the girls’ statements, but here’s one solution:
Two girls say that Mary placed fourth. If this is not true then Kitty was second (per Kitty’s statement) and Betty first (per Mary’s statement). But if Betty is first then Joan is second (per Ethel’s statement), which is a contradiction.
That means it’s true that Mary placed fourth, and it follows that Kitty is not second (per Kitty’s statement).
Hence Betty placed third (per Betty’s statement), Ethel placed fifth (per Joan’s statement), and Joan placed second (per Ethel’s statement). That leaves Kitty, who by process of elimination must have placed first.
From Problem Omnibus, 1960.
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