#DILR-6 (IMS)

Mr. Trump has a number of coins with him. Each coin has two sides, named ‘H’ and ‘T’. He plays a game, which begins with a number of coins all facing either ‘H’ or ‘T’.If the coins face ‘H’ initially, the target of the game is to make all the coins face ‘T’ at the end. Similarly, if the coins face ‘T’ initially, the target of the game is to make all the coins face ‘H’ at the end.The game consists of a number of moves. In each move, Mr. Trump has to flip exactly three coins (from ‘H’ to ‘T’ or from ‘T’ to ‘H’, as the case might be).

1) Mr. Trump begins the game with four coins all facing "T". What is the minimum number of moves he need to meet the target of the game?
(a) 2    (b) 3    (c) 4      (d) More than 4

2)Mr. Trump begins the game with five coins,all facing "H".What is the minimum number of moves he need to meet the target of the game? (Write "0" if the target cannot be achieved).
3)ADDITIONAL INFORMATION(for question 3 and 4):- Mr Trump now flips five coins in each move, instead of three. All other rules of the game remain unchanged.
Mr Trump begins the game with six coins, all facing "H".What is the minimum number of moves he needs to meet the target of the game?
(a) 2      (b)4      (c)5         (d)6

4)Mr Trump begins the game with six coins, all facing "H" and achieves the target in minimum possible moves. What is the absolute value of the difference between the number of coins that face "H" and the number of coins that face "T" just before he makes the last move?

SOLUTION-1) Mr Trump has 4 coins,all facing "T" i.e, TTTT
Now he can flip any three of them,
1- HHHT
2- HTTH
3- THTT
4- HHHH
option c will be the answer.

2) Now Mr Trump has 5 coins all facing "H" i.e, HHHHH
Now he can flip any three of them,
1- HHTTT
2-TTHTT
3-HTHHH
4-THTHH
5-HHHHH
 Hence "5" will be the answer.

Now what we are doing here is alternatively fixing one of the coins.
Suppose in the first question,we have to change all TTTT into HHHH but we can flip only 3 coins,so (4-3 = 1),we will alternatively fix H and T according to what it has asked.
Similarly, in question 2,we have five coins but we can flip only 3,so 5-3=2
possibilities are 2H,2T and 1H1T.
Now let's apply the same logic in question 3 and 4.

3)Now Mr Trump can flip 5 coins instead of 3 and we have total of 6 coins.
So difference here is ( 6 - 5 = 1).
  HHHHHH1-HTTTTT  (H fix)
2-THHHHT  (T fix)
3-HHTTTH   (H fix)
4-TTTHHT   (T fix)
5-HHHHTH  (H fix)
6-TTTTTT    (T fix)
Hence "6" moves will be our answer.
So the logic works fine.

4) Difference=|5-1|=4 ANS