Nim Game - Problem
The Ultimate Nim Game Challenge!
Imagine you're sitting across from your friend with a pile of stones between you, about to engage in one of the oldest strategic games known to humanity - Nim! 🪨
Here's how it works: You have a heap containing
Your Mission: Given the number of stones
Input: An integer
Output:
Example: If there are 4 stones, no matter what you do (take 1, 2, or 3), your opponent can always take the remaining stones and win!
Imagine you're sitting across from your friend with a pile of stones between you, about to engage in one of the oldest strategic games known to humanity - Nim! 🪨
Here's how it works: You have a heap containing
n stones on the table. You and your friend take turns removing stones, and you go first. On each turn, a player must remove between 1 to 3 stones from the heap. The player who takes the last stone wins the game! 🏆Your Mission: Given the number of stones
n, determine if you can guarantee a win assuming both players play optimally (meaning everyone makes the best possible move at each turn).Input: An integer
n representing the initial number of stonesOutput:
true if you can guarantee a win, false otherwiseExample: If there are 4 stones, no matter what you do (take 1, 2, or 3), your opponent can always take the remaining stones and win!
Input & Output
example_1.py — Small winning position
$
Input:
n = 1
›
Output:
true
💡 Note:
You can take 1 stone and win immediately since you took the last stone.
example_2.py — Classic losing position
$
Input:
n = 4
›
Output:
false
💡 Note:
No matter how many stones you take (1, 2, or 3), your opponent can take all remaining stones in their turn. Take 1→3 left (opponent takes all), Take 2→2 left (opponent takes all), Take 3→1 left (opponent takes it).
example_3.py — Force opponent into losing position
$
Input:
n = 5
›
Output:
true
💡 Note:
You can take 1 stone, leaving 4 stones. Now your opponent is in a losing position (multiple of 4), and no matter what they do, you can win.
Visualization
Tap to expand
Understanding the Visualization
1
Pattern Discovery
Test small values to discover the losing pattern
2
Strategic Analysis
Understand why multiples of 4 are trapped positions
3
Optimal Strategy
Always leave your opponent with a multiple of 4 stones
Key Takeaway
🎯 Key Insight: Positions where n % 4 = 0 are losing positions because any move you make can be countered to maintain the opponent's advantage. The game becomes a race to force your opponent into these 'trap' positions!
Time & Space Complexity
Time Complexity
O(1)
Single modulo operation
✓ Linear Growth
Space Complexity
O(1)
Only uses a constant amount of extra space
✓ Linear Space
Constraints
- 1 ≤ n ≤ 231 - 1
- Both players play optimally
- You always go first
💡
Explanation
AI Ready
💡 Suggestion
Tab
to accept
Esc
to dismiss
// Output will appear here after running code