Taro, Jiro, and Hanako played shogi (Japanese chess) and the ranking of the three was decided.
Anyone in the three says a lie about the ranking of the upper rank person than oneself and we do not know the talk about the ranking of the lower rank than oneself is the truth nor lie.
Taro said, "Jiro was not the third place."
Jiro said, "Hanako was not the third place."
Find the ranking of the three.
Anyone in the three says a lie about the ranking of the upper rank person than oneself and we do not know the talk about the ranking of the lower rank than oneself is the truth nor lie.
Taro said, "Jiro was not the third place."
Jiro said, "Hanako was not the third place."
Find the ranking of the three.
Answer
Supposing Jiro has said truth, Jiro is a higher rank than Hanako and since Hanako will not be the 3rd place, the ranking of the three is 1st Jiro, 2nd Hanako, 3rd Taro.
According to this assumption it turns out that Taro tells the truth on the upper order person.
Then we can find that Jiro has said a lie.
Therefore the ranking of Hanako is determined as third.
Since Taro has said the truth, Taro's order is upper than Jiro.
Then 1st Taro, 2nd Jiro, 3rd Hanako.
1st=Taro, 2nd=Jiro, 3rd=Hanako
Solution
Start considering the talk of Jiro whose name comes out most.
Supposing Jiro has said truth, Jiro is a higher rank than Hanako and since Hanako will not be the 3rd place, the ranking of the three is 1st Jiro, 2nd Hanako, 3rd Taro.
According to this assumption it turns out that Taro tells the truth on the upper order person.
Then we can find that Jiro has said a lie.
Therefore the ranking of Hanako is determined as third.
Since Taro has said the truth, Taro's order is upper than Jiro.
Then 1st Taro, 2nd Jiro, 3rd Hanako.
