Did you wait for the cucumber to ripen fully? When ripe they are yellow and starting to shrivel. Anything you would want to eat is too young to have viable seed yet.

George

Some cukes get bright orange when ripe. Once ripe, you should still bring them in and let them sit for another month before removing the seeds. Then the seeds must be fermented like tomato seeds.

Beets and carrots are not the easiest food crops to get seeds from.
Beets are biennial so they need two seasons to make seeds. Once they flower, they need to be bagged or isolated by a few miles since they are wind pollinated.

Carrots are also a biennial. If you have Queen Anne's Lace where you live, it is difficult to save seeds since they cross pollinate. If there's none, you only need like a 1/2 mile for seed purity.
Remy

Will seed from beets in the first year be fertile? My beets want to make flowers but will they be any good?
When should carrot seeds be harvested? The umbrels are closing but not all seeds seem to be formed or brown.
Thanks!

Hi T.,
You are lucky if your beets want to make flowers. Sometimes biennials will do that and with the whack summer we've had, I can see them flowering. Yes, the seeds from the flowers will be good, but you must bag them because of the high cross pollination rate. Since they need to be pollinated by separate plants, you must make the flower heads of a few plants be together by tying together close enough to get big paper bags over them together. Then you need to seal up the bottom of the bags to keep out stray insects or air born pollen. It really seems like a pain in the you know what, lol. Seed to Seed recommends cotton batting wrapped around the stalks and bag and taped.
You can of course hope nothing with in a few miles of you has also bloomed and just save the seeds.

The carrot seeds will eventually turn brown, just keep an eye on them. Some seeds may not have formed if pollination wasn't successful so you can get umbels partially filled with seeds.
Remy