I tried to solve this problem. But may be not getting it right... I believe my algo is very close to correcrt.. Any suggestion would be highly appreciated...

This is what i did.

//mapped all the 12 sticks to  bit of mask

//ith bit in mask  represents the stick is not removed  if 0 , and removed if 1

bool iswin(mask,mouse,cheese)

{

      // checked weather the mouse is reachable to cheese in present mask condition using dfs

      if(reachable)

          return false..

      flag = 0;

      

      for(i=0;i<12;i++)

       {

if(!(mask&(1<<i)))   // checked if the ith stick is already removed or not... if not it goes to next step..

                  {

                       if(!iswin(mask|(1<<i))) // checks is it a loosing position if ith stick is removed by the player..

                          {

                                flag=1;      // if he gets a reachable loosing position ...he is in winning position for sure....

                                break;

                          }

                  }

       } 

       return flag;

}

if SOHA is in winning position he is the winner else it is TARA