Suppose in a game with a pile containing a large number of chips, you can remove any number from 1 to 6 chips at each turn. what is the winning strategy?

the winning strategy is to take 1 chip, leaving our opponent with  the losing position of 5 chips.

Step-by-step explanation:

suppose we start with 6 chips.

* If we take 1 chip, we leave our opponent with 5 - which we showed  

  was a losing position for him.

* If we take 2 chip (leaving 4), our opponent will take 3 - we lose.

* If we take 3 chip (leaving 3), our opponent will take 2 - we lose.

So our winning strategy is to take 1 chip, leaving our opponent with  

the losing position of 5 chips.