From e93192d274cfa782156f40c23a8cf605ac93a626 Mon Sep 17 00:00:00 2001
From: roshankumar447 <roshankumar.591978@gmail.com>
Date: Sat, 7 Nov 2026 20:48:59 +0530
Subject: [PATCH] feat: add nim-game algorithm with tests

---
 .../java/com/thealgorithms/maths/NimGame.java | 23 ++++++++++++++++++
 .../com/thealgorithms/maths/NimGameTest.java  | 24 +++++++++++++++++++
 2 files changed, 47 insertions(+)
 create mode 100644 src/main/java/com/thealgorithms/maths/NimGame.java
 create mode 100644 src/test/java/com/thealgorithms/maths/NimGameTest.java

diff --git a/src/main/java/com/thealgorithms/maths/NimGame.java b/src/main/java/com/thealgorithms/maths/NimGame.java
new file mode 100644
index 000000000000..f9df6a37c69b
--- /dev/null
+++ b/src/main/java/com/thealgorithms/maths/NimGame.java
@@ -0,0 +1,23 @@
+package com.thealgorithms.maths;
+
+/**
+ * Nim Game: Two players take turns removing 1 to 3 stones from a pile.
+ * The player who removes the last stone wins. Returns true if the first
+ * player can guarantee a win given n stones.
+ *
+ * <p>Key insight: if n is a multiple of 4, the second player always wins
+ * because whatever the first player takes (1-3), the second player can
+ * always take enough to leave another multiple of 4.
+ *
+ * <p>Time complexity: O(1), Space complexity: O(1)
+ *
+ * @see <a href="https://leetcode.com/problems/nim-game/">LeetCode #292</a>
+ */
+public final class NimGame {
+    private NimGame() {
+    }
+
+    public static boolean canWinNim(int n) {
+        return n % 4 != 0;
+    }
+}
diff --git a/src/test/java/com/thealgorithms/maths/NimGameTest.java b/src/test/java/com/thealgorithms/maths/NimGameTest.java
new file mode 100644
index 000000000000..58e342df176f
--- /dev/null
+++ b/src/test/java/com/thealgorithms/maths/NimGameTest.java
@@ -0,0 +1,24 @@
+package com.thealgorithms.maths;
+
+import static org.junit.jupiter.api.Assertions.assertFalse;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import org.junit.jupiter.api.Test;
+
+public class NimGameTest {
+
+    @Test
+    public void testFirstPlayerWins() {
+        assertTrue(NimGame.canWinNim(1));
+        assertTrue(NimGame.canWinNim(2));
+        assertTrue(NimGame.canWinNim(3));
+        assertTrue(NimGame.canWinNim(5));
+    }
+
+    @Test
+    public void testSecondPlayerWins() {
+        assertFalse(NimGame.canWinNim(4));
+        assertFalse(NimGame.canWinNim(8));
+        assertFalse(NimGame.canWinNim(12));
+    }
+}