awesome :) On Wed, Jul 7, 2010 at 9:07 AM, Dave <[email protected]> wrote:
> There are 6 cases to consider (we can list them but we don't know > which one applies): > 1. Initially, all 4 coins are tails. > 2. Initially, all 4 coins are heads. > 3. Initially, 3 of the coins are heads, 1 is tails. > 4. Initially, 3 of the coins are tails, 1 is heads. > 5. Initially, 2 diagonal coins are heads, the others are tails. > 6. Initially, 2 adjacent coins are heads, the others are tails. > > After every flip, we ask if all coins are heads. > If so we have solved the puzzle, otherwise we continue to the next > step. > We proceed as follows: > 1. Flip all coins. > At this point, we have solved the puzzle if case 1 applies. > 2. Flip all coins. > At this point, we have solved the puzzle if case 2 applies. > 3. Flip any two diagonal coins. > 4. Flip all coins. > At this point, we have solved the puzzle if case 5 applies. > 5. Flip any two adjacent coins. > 6. Flip all coins. > 7. Flip any two diagonal coins. > 8. Flip all coins. > At this point, we have solved the puzzle if case 6 applies. > Thus, we are left with cases 3 and 4. > 9. Flip any one coin. > 10. Flip all coins. > At this point, if the one coin we flipped in step 9 was the odd one, > we have solved the puzzle. > Otherwise, the current configuration has 2 heads and 2 tails. > 11. Flip any two diagonal coins. > 12. Flip all coins. > At this point, we have solved the puzzle if the result of step 10 was > diagonal pairs. > 13. Flip any two adjacent coins. > 14. Flip all coins. > 15. Flip any two diagonal coins. > 16. Flip all coins. > At this point, we have solved the puzzle. > > Dave > > On Jul 5, 11:10 pm, Jitendra Kushwaha <[email protected]> > wrote: > > Seems tough to do as every time we dont know which coins we flipped in > the > > previous move > > > > We can perform all the four operation one by one in circular fashion and > we > > will have probabilitty of getting all head up at some time. > > this is because even if table rotated at random, each of the for step > will > > do different thing from previous step. > > > > I have not proofed it rigorously. It seems to be a solution to me > > > > comments appreciated... > > > > -- > > regards > > Jitendra > > -- > You received this message because you are subscribed to the Google Groups > "Algorithm Geeks" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]<algogeeks%[email protected]> > . > For more options, visit this group at > http://groups.google.com/group/algogeeks?hl=en. > > -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
