Careful, being unguessable is
not one of the properties required of a UUID. All a UUID guarantees is that two UUIDs
generated by the specified procedure will never match, even if they're generated by different computers not in communication with each other. But it does
not guarantee that an attacker cannot generate the same UUID generated by somebody else if they follow a
different procedure.
It's the difference between avoiding collisions between cooperating entities, and avoiding collisions from malicious entities.
For example, a version 1 UUID is just the combination of the computer's MAC address and the current time. This is sufficient to guarantee uniqueness (as long as you don't duplicate MAC addresses, and you wait at least 100 nanoseconds between generating successive UUIDs) but will be pretty easy to guess if you have a rough idea of when the UUID was generated and which manufacturer might have made the NIC on the machine where it was generated.
More abstractly, a version 4 UUID is just a couple of identifying bits and 122 random bits, but the nature of the random bits is not specified. Your UUID generator may well use a PRNG that is not cryptographically secure, which could still be good enough for cooperative uniqueness, but not good enough to avoid predictability. (For example, a PRNG seeded with the machine's MAC address and boot time would fit this.)
In short, don't rely on a UUID being secret unless you know exactly how it's being generated, all the way down to the underlying random number generator. And if you're going that far, you might as well just read 16 bytes from /dev/random and be done with it.