Puzzle: lishogi.org/training/jYTwE
Full description in study - lishogi.org/study/jMhEDU7r .
With the gold drop on 43, the king can run on 32.
Anyway, a lot of "3-moves mate" are actually a 5-moves mate.
Did You mean king can run to 31?
G*43 K31 S32 K22, also G*43 K31 S42 K22 and no matter what piece goes to 33, knight will take and there is no mate.
For example, this puzzle is actually a 5-moves mate: lishogi.org/training/iDmFM
The correct answer is +R-24 Kx24 B*35
but if gold takes: +R-24 Gx24 B*31 (white must interpose a piece) L*22 +Rx22