Rather than looking at existing categories of cameras, Sigma says it's aimed to make a user-oriented camera that's designed to be flexible, adaptable and fun to use.

It gains a 61MP BSI CMOS sensor, providing a more stills-focused platform than the original fp 24MP L-mount mirrorless camera. Also, as B would prefer Nim sum of zero for A‘s turn, he would then play a move so as to make the Nim Sum zero again (which is always possible, as mentioned above).The Sigma fp L is a high-resolution development of the company's compact full-frame interchangeable lens camera.

So, as the Nim Sum is initially zero, whatever number of items A removes the new Nim Sum would be non-zero (as mentioned above).

If the XOR sum of ‘n’ numbers is non-zero then there is at least a single approach by which if you reduce a number, the XOR sum is zero.Īs we know, in this case if played optimally B wins, which means B would always prefer to have Nim sum of zero for A‘s turn.

If the XOR sum of ‘n’ numbers is already zero then there is no possibility to make the XOR sum zero by single reduction of a number.

Otherwise, if the Nim-Sum evaluates to zero, then player A will lose definitely.”įor the proof of the above theorem, see- Ĭouple of deductions about bitwise XOR necessary for understanding the Optimal Strategy: “If both A and B play optimally (i.e- they don’t make any mistakes), then the player starting first is guaranteed to win if the Nim-Sum at the beginning of the game is non-zero. Nim-Sum : The cumulative XOR value of the number of coins/stones in each piles/heaps at any point of the game is called Nim-Sum at that point. In fact, we can predict the winner of the game before even playing the game !

The initial configuration of the piles/heaps.

So, we can conclude that this game depends on two factors. This time the initial configuration was different from the previous one. That factor is the initial configuration of the heaps/piles. Thus, there must be another factor which dominates the result of this simple-yet-interesting game. But how? We know that this game depends heavily on which player starts first. Will A win again as he has started first ? Let us see.Ī made the first move, but lost the Game. Let us again play the game, starting from A, and this time with a different initial configuration of piles. So does the player who starts first will win everytime ? Let us now play again, with the same configuration of the piles as above but this time B starting first instead of A.ī Won the match (Note: B made the first move)īy the above figure, it must be clear that the game depends on one important factor – Who starts the game first ? So was A having a strong expertise in this game ? or he/she was having some edge over B by starting first ? See the below figure for clear understanding of the whole game play.Ī Won the match (Note: A made the first move) ”įor example, consider that there are two players- A and B, and initially there are three piles of coins initially having 3, 4, 5 coins in each of them as shown below.

The player who cannot move is considered to lose the game (i.e., one who take the last stone is the winner). In each turn, a player can choose only one pile and remove any number of stones (at least one) from that pile. “ Given a number of piles in which each pile contains some numbers of stones/coins. The Game of Nim is described by the following rules. We strongly recommend to refer below article as a prerequisite of this.Ĭombinatorial Game Theory | Set 1 (Introduction) K maximum sum combinations from two arrays.Minimum product of k integers in an array of positive Integers.Median of Stream of Running Integers using STL.Median in a stream of integers (running integers).Longest Increasing Subsequence Size (N log N).Maximum size square sub-matrix with all 1s.Maximum size rectangle binary sub-matrix with all 1s.Top 20 Dynamic Programming Interview Questions.Game of N stones where each player can remove 1, 3 or 4.Find the winner of the game with N piles of boxes.Minimax Algorithm in Game Theory | Set 5 (Zobrist Hashing).Minimax Algorithm in Game Theory | Set 4 (Alpha-Beta Pruning).Minimax Algorithm in Game Theory | Set 3 (Tic-Tac-Toe AI – Finding optimal move).Minimax Algorithm in Game Theory | Set 1 (Introduction).Combinatorial Game Theory | Set 4 (Sprague – Grundy Theorem).Combinatorial Game Theory | Set 3 (Grundy Numbers/Numbers and Mex).Combinatorial Game Theory | Set 1 (Introduction).Combinatorial Game Theory | Set 2 (Game of Nim).ISRO CS Syllabus for Scientist/Engineer Exam.ISRO CS Original Papers and Official Keys.GATE CS Original Papers and Official Keys.

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