Two kids are liars, three are telling the truth. Jane: "if onln Joey doesn't lie,then either Jane or John do" joey:"jack lies as does Jane or Julia, John: if Julia is telling the truth then Jane or joey do as well jack: If you round up Jane, Joey,and john you will have at least one liar the compulsive liar are?
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This is not the original wording of the puzzle.
In the original puzzle, Joey says "Jack lies, as does Jane OF Julia". This puzzle says "Jane OR Julia"
That single letter mistake turns a very complex puzzle into an extremely easy puzzle.
The answer to the original wording is Joey and Julia are the liars.
To determine the compulsive liars, let's analyze each person's statements:
1. Jane says, "If only Joey doesn't lie, then either Jane or John does."
If we assume Jane is telling the truth, it contradicts the condition that only Joey doesn't lie. Therefore, Jane is lying.
2. Joey says, "Jack lies as does Jane or Julia."
If we assume Joey is telling the truth, it means Jack lies. This is consistent with the statement made by Jane, who we already know is lying. Therefore, Joey is telling the truth.
3. John says, "If Julia is telling the truth, then Jane or Joey do as well."
Since we have established that Jane is lying, we conclude that Julia is not telling the truth. Consequently, John's statement is false.
4. Jack says, "If you round up Jane, Joey, and John, you will have at least one liar."
Based on the information we have gathered so far, Jack's statement seems plausible, as we have identified Jane and John as liars. However, to be certain, we need to consider Joey's statement as well.
Considering all the statements, we have determined that the compulsive liars are Jane and John.
To determine the compulsive liar(s) among Jane, Joey, John, and Jack, let's analyze their statements and find any contradictions.
1. Jane says, "If only Joey doesn't lie, then either Jane or John do." This implies that at least one of Jane or John is lying.
2. Joey says, "Jack lies, as does Jane or Julia." This means either Jack, Jane, or Julia is lying.
3. John says, "If Julia is telling the truth, then Jane or Joey do as well." Therefore, if Julia is telling the truth, at least one of Jane or Joey is also telling the truth.
4. Jack says, "If you round up Jane, Joey, and John, you will have at least one liar." This means that there is at least one liar among Jane, Joey, and John.
Based on these statements, we can make some deductions:
- Jane and John cannot both be telling the truth since Jane says that at least one of them is lying, and John says that if Julia is telling the truth, then Jane or Joey is as well.
- If Julia is telling the truth, then at least one of Jane or Joey must be telling the truth, according to John's statement.
- Combining Jane's statement with John's, if Julia is telling the truth, then John must be lying, and Jane or Joey would be telling the truth.
- Jack's statement confirms that at least one of Jane, Joey, and John is lying.
Based on this analysis, we can conclude that the compulsive liar(s) among the four people are Jack and John, as their statements contradict the statements of the others.