Question

You have fox,grain and chicken and you need to cross river, how will you manage if you are only take one at a time with you.

Answer 1

A Stock Puzzle, subset of the Inventory Management Puzzle. You are a farmer taking a fox (or a wolf), a chicken (or a goose) and a sack of grain to market (don't ask why you're taking a fox to market) and you come across a river. The only way across the river is by a small boat, which can only hold at most you and one of the three items. Left unsupervised, the chicken will eat the grain or the fox will eat the chicken (however, the fox won't try to eat the grain, nor will the fox or the chicken wander off). What's the quickest way to get everything across the river?

The standard answer is:

Take the chicken across

Come back with the boat empty besides yourself

Take the grain (or the fox) across

Take the chicken back

Take the fox (or the grain) across

Come back with the boat empty besides yourself

Take the chicken across

This puzzle's primary difficulty to those new to the puzzle is in realizing that one must consider the possibility of taking an action that seems detrimental or a step back from their original goal in order to ultimately complete it.

May also appear with different animals and vegetables, such as wolves, sheep and cabbages. A "jealous husbands" (also known as cannibals and missionaries) variant has three couples trying to cross a river with a two-person rowboat, but none of the men will allow his wife to be alone with either of the other men on either side of the river (or, cannibals cannot outnumber missionaries, lest the latter attacked and eaten). This one can be solved in eleven steps.

This is an ancient puzzle. The oldest known example was found in Propositiones ad. Acuendos Juvenes, which dates to the late ninth century.

A more complicated version, but which operates on much the same principle, involves a barrier (usually a bridge), four people who all move at different rates, and some item that is required in order to cross the barrier (most often a flashlight). The puzzle is to get all the people across within a specified amount of time, which seems to be too short. Probably the most well-known version of this is:

Answer 2

first i will take the chicken 
then the fox but bring the chicken back 
then take the grain and leave the chicken alone 
at last take the chicken