You have been slain (Beta)
Layla is heartbroken because the one and only boyfriend she likes has cheated on her. Then, Layla asks Karina, a professional hitman, to slay her boyfriend. To make things edgy, Layla only gives Karina some clues instead of telling her directly. Karina tries to solve those clues given by Layla and eventually she meets five males whom she finds suspicious. Those five males are Clint, Alucard, Estes, Hayabusa, and Yunzhao. These are their claims:
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Clint: Yunzhao cheats
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Alucard: Clint does not cheat but he lies
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Estes: Clint and Alucard does not cheat
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Hayabusa: Estes does not cheat but I do
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Yunzhao: I do not cheat but Estes lies
Karina knows that only one male tells the truth.
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Who tells the truth?
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Who will be slain?
Note: Clint = 1, Alucard = 2, Estes = 3, Hayabusa = 4, Yunzhao = 5
Answer these problems by stacking the index given above respectively. For example, if the first answer is number 4 and the second answer is number 3, please submit the answer 43.
Author's note:
I've not been active here for long time. This is my original problem, in which the inspire comes from the game fandom in Instagram ^_^. Well, if there is an extant problem that looks similar or same, this is a pure accident. Regards.
Plus, I don't like to think a character's name, so I take the character's names from Mobile Legends. ROTFL
The answer is 51.
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1 solution
I've written the solution case by case before, maybe some of you may simplify my solution, for I already made this problem few weeks ago with the complete solution as well.
Make the table and negate each premise
Given that Karina knows that only one male tells the truth and one cheater
Case 1: Clint does not lie
Since Clint does not lie, thus Yunzhao cheats. Estes lies, hence either which Clint or Alucard cheats, which means at least there is a person among Clint or Alucard cheats. In this case, there will be at least two cheaters, which contradicts the fact that there is only one cheater.
Case 2: Alucard does not lie
Since Alucard does not lie, Clint does not cheat and he lies, which does not contradict to the fat. This implies that Yunzhao does not cheat either. Estes lies, hence either Clint or Alucard cheats, but since Clint does not cheat, then Alucard must cheat. Hayabusa lies, hence the premise Estes cheats is false and Hayabusa does not cheat is true holds. In this case, Alucard cheats, however, since Yunzhao lies, either Yunzhao cheats or Estes does not lie. But then, Yunzaho does not cheat and Estes lies, which contradicts each other.
Case 3: Estes does not lie
Since Estes does not lie, Clint and Alucard does not cheat. Clint lies, hence Yunzhao does not cheat. Consider to Alucard’s statement. Since Alucard lies, Clint cheats or he does not lie, but according to the fact, Clint does not cheat and he lies either, which contradicts each other.
Case 4: Hayabusa does not lie
Since Hayabusa does not lie, Estes does not cheat and Hayabusa admits himself that he cheats. Consider Estes’s statement. Since Estes lies, either which Clint or Alucard cheats, which takes the same contradicting case as the first case (i.e. there are at least two cheaters)
Case 5: Yunzhao does not lie
Since Yunzhao does not lie, he does not cheat and Estes lies. Clint lies, so Yunzhao does not cheat. Alucard lies, so either which Clint cheats or he does not lie. Since Clint lies, in order to hold the negation true, Clint cheats, which implies that Alucard does not cheat according to Estes’s statement, since he lies. Hayabusa tells lie, hence Estes cheats or Hayabusa does not cheat. The premise Estes cheats holds false and the premise Hayabusa does not cheat holds true. Thus, the statement holds true. Hence, Clint lies whereas Yunzhao tells the truth.