-
22#22 (So
23#23)
-
24#24 (So
25#25)
-
26#26 (
27#27)
-
28#28 (
29#29)
- Fibonacci sequence:
30#30 (for 31#31),
32#32 (Closed form? various ways to express it.
Discussed at the board.)
- Fibonacci variants (Discussed on the board).
- Cauchy equation:
33#33. (
34#34, for
rational 13#13. If 18#18 is defined on the reals, and is
continuous, then
34#34 everywhere). There
are variants of this equation involving multiplication instead
of addition...
- Josephus Problem: 21#21 rebels (let's say 35#35 for simplicity)
are trapped by the Romans and decide to kill themselves rather than
be captured. They form a circle and go around it, killing every other
person until one is left, who must commit suicide. As the lone spy
in the group, you'd like to position yourself to be the one person
left. What position do you stand in? (Note: in the original story,
the 41 rebels killed every third person and Josephus found the
right places for himself and an accomplice to stand in order to be
the last two people left).