There's one in-game puzzle of sorts that yields gems; the puzzle isn't listed here, but the gems in the set are.
a flawless diamond
a stunning sapphire
a violet garnet
a green spinel
a golden topaz
a oversized emerald
a white jade
a star rose quartz
a blue quartz
a blue jasper
a brilliant amethyst
a brilliant ruby
a citrine stone
a white pearl
a turquoise stone
a malachite stone
a black opal