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 <jitendra.th...@gmail.com> 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 algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
