Type it, don't hunt for it.
Two games on the same 2-set (두벌식) keyboard the quiz uses. Play them with your own keyboard or tap the keys on screen.
Falling jamo
Letters drop down the column of the key that types them. Hit the key while the letter is crossing the line. Three misses ends the round — it gets faster the longer you last.
Guided typing
The next key lights up, you press it, and the syllable assembles as you go. Drill the bare letters first, then real vocabulary — with the hints switched off once you stop needing them.