Thank you honeybadger, you are right.
In puzzle 3789, 4. ... 14-19 and 14-20 are both winning. But I played 14-20, it says it's wrong.
Russian puzzel 528...you're forced to make a losing move after which you are a passenger and white executes the shot.
It seems as the position needs to be reversed...i.e. the puzzle player should have the white pieces and find the forcing move and following (nice) shot.
@dg As for Russian puzzle #528, I agree with you.
There is a particular theme in draughts puzzles: countering opponent plans. In #528 black chooses "safe" option which white refutes by a cascade of sacrifices and a shot. If that puzzle was intended for verifying calculation skills, it should be set differently.
In #528 black can equalize by making exchange: e7-d6, f8-e7, and taking backwards h6xf8.
In puzzle 3789 it isn't winning if you play 4. ... 14-20. White can give a king with 47-41 and 30-25 is draw.
@dg and @kalnap
I agree with you. d2-e3 is draw says Aurora Borealis, c1-b2 is losing and the 5th 'best' move. If you change colors, the startingmove c5-d4 is one of the best moves for black, but not the only one. So the puzzle is not good and will be disabled.
The puzzle would be better with the first mistake for white playing c1-b2. And than black executing the shot as shown is this puzzle.
Best of wishes