Eight Claims About the Tally
Eight statements are written on a card, and each speaks about $T$, the total number of true statements on the card (including itself). 1. $T$ is a prime number. 2. $T$ is a perfect square (0 counts as one). 3. $T$ is even (0 counts as even). 4. $T$ is at least 5. 5. $T$ is a multiple of 3 (0 counts as a multiple of 3). 6. $T$ is at most 3. 7. $T$ is 6 or 8. 8. $T$ is a multiple of 4 (0 counts as a multiple of 4). Each statement is true or false according to its content. What is $T$?
Related problems
Source: Original problem written for AxiomIQ, in the tradition of self-referential truth-counting puzzles.