**Puzzle 68.** Borrowing a notational convenience from the [temporal logic of actions](https://en.wikipedia.org/wiki/Temporal_logic_of_actions), I like to notate the "next" value of a variable \\(x\\) using prime notation, \\(x'\\). So we can say that \\((x, y, z) \le (x', y', z')\\) iff \\(\exists c \in \mathbb{N}. x = 2cx' \land y = cy' \land cz = z'\\). This is (**EDIT:** not) the same rule as Marius' in #13, except the common factor \\(c\\) has not been eliminated, and the prime is used in the opposite convention. (**EDIT:** No, Marius' was closer to being correct than mine. See #16 for something that's hopefully completely correct.)

**Puzzle 70.** Thanks to prime notation, we can flip the reaction by redefining "prime" to mean "previous". Symmetrically, we could prime un-primed variables, and de-prime primed variables.

**Puzzle 70.** Thanks to prime notation, we can flip the reaction by redefining "prime" to mean "previous". Symmetrically, we could prime un-primed variables, and de-prime primed variables.