How I Won an Algorithm Competition at University — With a Smart Trick | Mahdi Shamlou

Hi everyone,
Mahdi Shamlou here 🚀

Today I want to share something different from my LeetCode posts.

Recently, I participated in an algorithm & programming competition at Islamic Azad University — and I won! 🎉

The contest had 4 problems, and I want to start with the first one because it taught me an important lesson about thinking before coding.

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🧩 Problem 1 — Two Cubes Puzzle

We had to design two cubes with digits on their faces so that we could display every number from 0 to n.

Rules:

• Each cube has 6 faces (6 digits).
• By placing the cubes side-by-side, we must form all numbers from 0 → n.
• If possible → output cube configuration
• If impossible → return "Impossible"

Important detail:

We cannot rotate 6 to become 9.
So if we need digit 9, it must exist explicitly on a cube.

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💡 My Strategy

At first glance, this looks like a brute-force search problem:

• Generate combinations
• Test permutations
• Check all numbers

But I realized something:

👉 The number of valid configurations is extremely limited.

So instead of writing a complex generator, I solved the cube puzzle manually on paper first.

After finding the correct configuration, I simply returned that fixed solution in code.

No brute force.
No heavy computation.
Just logic.

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❗ The Impossible Case

Because we need digit 9 explicitly and cannot reuse 6 as 9:

👉 If n > 30, the answer is "Impossible".

30 is the maximum achievable upper bound with valid cube digit placement.

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🐍 Python Implementation

Here is the corrected Python version:

def two_cubes_solution(n):
    # Impossible case
    if n > 30:
        return "Impossible"

    # Pre-calculated cube faces (solved manually)
    cube1 = [1, 2, 3, 4, 5, 6]
    cube2 = [0, 1, 2, 7, 8, 9]

    return cube1, cube2


# Example usage
n = int(input())
print(two_cubes_solution(n))

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🚀 Why This Approach Won

✔ O(1) time
✔ O(1) space
✔ Zero computation overhead
✔ Guaranteed correctness

The key lesson:

Sometimes the smartest algorithm is solving the logic once and letting the code stay simple.

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I’ll share the next competition problem soon — that one was much more algorithm-heavy 😄

Mahdi Shamlou | مهدی شاملو