Red 2002 MIT Mystery Hunt

## TRUE AND FALSE

"One reason I was able to excel in the industry," your uncle once wrote, "is that I consider see every option so clearly. True and false, black and white, cut and dried, in and out, kit and kaboodle."
1. The only way to get the intended magic word is to chop up the forty answers into four equal groups, interpreting each as a letter using a ten-bit encoding
2. The only way to get the intended magic word is to chop up the forty answers into five equal groups, interpreting each as a letter using an eight-bit encoding
3. The only way to get the intended magic word is to chop up the forty answers into eight equal groups, interpreting each as a letter using a five-bit encoding
4. The statement listed three statements prior to this one is true.
5. Of the statements that read "The statement listed three statements prior to this one is true", at least two are true.
6. The statement listed three statements prior to this one is true.
7. The statement listed three statements prior to this one is true.
8. Exactly one-sixth of the true statements occur between the first statement and this one, inclusive.
9. There is a sequence of four consecutive false answers, but there are no longer sequences.
10. There is a sequence of five consecutive false answers, but there are no longer sequences.
11. There is a sequence of six consecutive false answers, but there are no longer sequences.
12. Of the statements numbered with a multiple of twelve, an odd number are true.
13. Of the statements numbered with a multiple of thirteen, an even number are true.
14. Of the previous statement and the next statement, exactly one is true.
15. The next statement would be just as true as it is now if it were replaced with: "Each statement that begins with the phrase 'Exactly one-sixth' is true".
16. The previous statement would be just as true as it is now if it were replaced with: "Each statement that begins with the phrase 'Exactly one-sixth' is true".
17. This very statement would be just as true as it is now if it were replaced with: "Each statement that begins with the phrase 'Exactly one-sixth' is true".
18. Every statement whose number yields a remainder of three when divided by six is false.
19. Of the previous statement and the next statement, exactly one is true.
20. Exactly half of the true statements occur between the first statement and this statement, inclusive.
21. The previous statement and the next statement are either both true or both false.
22. There are more true statements in the last quarter of this list than there are in the first quarter.
23. There are more true statements in the last quarter of this list than there are in the second quarter.
24. Of this statement and the two previous statements, an odd number are true.
25. When I told three people the magic word and asked which of the five Zenner card symbols came to mind, a majority of them chose the square.
26. When I told three people the magic word and asked which of the five Zenner card symbols came to mind, a majority of them chose the three wavy lines.
27. When I told three people the magic word and asked which of the five Zenner card symbols came to mind, a majority of them chose the circle.
28. When I told three people the magic word and asked which of the five Zenner card symbols came to mind, a majority of them chose the star.
29. This statement is part of the strictly longest consecutive stretch of true statements.
30. Of the statements numbered with a multiple of six, exactly one-half are true.
31. Of this statement and the two that follow, exactly one is true.
32. Of the statements numbered with a power of two, exactly half are true.
33. The statement listed ten statements prior to this one is true.
34. If the previous two statements are listed in the reverse order and all statements retain their truth values, then the result is still consistent.
35. Of the statements numbered with a multiple of seven, exactly one is true.
36. Of the statements numbered with a multiple of nine, none are true.
37. The thirtieth statement is as true as this statement.
38. Exactly one-sixth of the true statements occur between this statement and the last statement, inclusive.
39. Both this statement and the next one are true.
40. Exactly one-half of the statements numbered with a multiple of five are true.