Nine Interlocking Claims
Nine statements are written in a list. Each is true or false according to what it says. 1. Statements 5 and 6 are both true. 2. Exactly 2 of these nine statements are true. 3. Statements 2 and 9 are both false. 4. At least two of statements 3, 7 and 8 are true. 5. Statements 7 and 9 are both true. 6. If statement 9 is true, then statement 7 is false. 7. Statements 2 and 8 are both true. 8. Exactly one of statements 1 and 6 is true. 9. Statements 4 and 6 are both false. How many of the nine statements are true?
Related problems & prerequisites
Worth solving first
- Eight Claims About the Tally 5.0/10
- Five Queens Rule the Board 5.0/10
Source: Original puzzle written for AxiomIQ; the format of statements referring to each other is a staple of recreational logic.