The trick to this puzzle is that you can keep fox and grain together. So the solution would be
The man will start with the chicken. He will go to the other side of the river with the chicken. He will keep chicken there and will return back and will take grain with him on the next turn. When he reaches the other side he will keep the grain there and will take chicken back with him.
Now we will take fox and will keep the fox at the other side of the river along with the grain. He will return back and will take chicken along with him. This way they all will cross the river.
Just to give a clear picture
M - Man
C- Chicken
F- Fox
G- Grain
M C F G ------------------------------------------------------------------------------- other side
F G ------------------------------------------------------------------------------------- M C
Man return back
F G M ---------------------------------------------------------------------------------- C
F ----------------------------------------------------------------------------------------G M C
Man returns back with Chicken
F C M ----------------------------------------------------------------------------------- G
Takes Fox with him
C ---------------------------------------------------------------------------------------- F G M
Man returns back
C M ------------------------------------------------------------------------------------- F G
Takes chicken with him
-------------------------------------------------------------------------------------- C M F G
The man will start with the chicken. He will go to the other side of the river with the chicken. He will keep chicken there and will return back and will take grain with him on the next turn. When he reaches the other side he will keep the grain there and will take chicken back with him.
Now we will take fox and will keep the fox at the other side of the river along with the grain. He will return back and will take chicken along with him. This way they all will cross the river.
Just to give a clear picture
M - Man
C- Chicken
F- Fox
G- Grain
M C F G ------------------------------------------------------------------------------- other side
F G ------------------------------------------------------------------------------------- M C
Man return back
F G M ---------------------------------------------------------------------------------- C
F ----------------------------------------------------------------------------------------G M C
Man returns back with Chicken
F C M ----------------------------------------------------------------------------------- G
Takes Fox with him
C ---------------------------------------------------------------------------------------- F G M
Man returns back
C M ------------------------------------------------------------------------------------- F G
Takes chicken with him
-------------------------------------------------------------------------------------- C M F G
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