can u explain me how BOB is winning when N=7;
accrding to me-
first chance:
bob would take out from N prime number 5…ie…(N-5)so new N is 2.
second chance:
alice would take out 1 and would certainly WIN…
plz help me out…
can u explain me how BOB is winning when N=7;
accrding to me-
first chance:
bob would take out from N prime number 5…ie…(N-5)so new N is 2.
second chance:
alice would take out 1 and would certainly WIN…
plz help me out…
Here is detailed explanation to your NUMGAME2 problem.
Consider each value of N as a position. And positions have following properties:
All terminal positions are losing.
If a player is able to move to a losing position then he is in a winning position.
If a player is able to move only to the winning positions then he is in a losing position.
We will solve this problem from Bob’s point of view since he is the one to play first.
Now N = 1 (terminal position, property 1) is a
losing position for bob because he
has to play first and he can not
make a move. So N = 1 is losing position.
For N = 2, Bob can subtract 1 form N and manage to move to a losing position and since its now Alice’s chance and she is now at losing position Alice will loose and Bob will win (Property 2). So N = 2 is winning position.
Remember this is all from Bob’s point of view.
For N = 3, Bob can subtract 2 from N and get to losing position (i.e. N = 1) and wins the game.
For N = 4, subtract 3.
So far we have established that,
N L/W
1 L
2 W
3 W
4 W
Consider N = 5, Bob can subtract {1, 2, 3} from the N
Subtract 1, N = 4 Winning position
Subtract 2, N = 3 Winning position
Subtract 3, N = 2 Winning position
So Bob is not able to move to a losing position, and there by he loses (property 3).
Hence N = 5 is a losing position.
If we go on like this we will see that positions {1, 5, 9, 13, 17…} are losing position for Bob. That is N = {4 * x + 1, x = 0, 1, 3,…}.
Therefore for N = 7 Bob wins. He can subtract 3 and manage to move to a losing position. And by property 2 he wins the game.
Hope it helps, Best Luck
And Please Do Not Spam the forum with repeated questions.
got it thnx…
7-3 = 4 is a winning position for alice,then how BOB wins??please answer.