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Superglue (cyanoacrylate) will work.
I would think CA glue (Superglue) would do the trick as CCC suggested. Perhaps you could also get a small bottle of activator to help bond the glue more quickly and not have to worry about it being too fiddly after you initially glue it.
Mix some up in the back yard - about half a bucket of sand and half a bucket of cement. Mix water in until you get the right consistency.
Place the broken piece carefully in a wooden frame about 25cm x 25cm (or you could use a baseplate edged with 2x4 bricks), and be sure to put the broken pieces next to each other.
Pour the cement into the frame carefully - you don't want to slop it in and risk moving the broken piece!
Leave it to set for a few days.
Pop it out of the frame and use it as a door wedge or paperweight, then go buy a new piece.