Assil vs Ramses II

Written by Iyed Baassou

Problem Statement

English
Arabic
French

Solution

* We denoted the given number of boxes as .

We can notice that the number of boxes in layer is

Thus we can find the number of layers by subtracting , , , ... , from until it's negative.

This can be reformulated as the greatest such that

We can implement this with a while loop with the condition sum + i**2 <= x and we keep adding to sum and increasing the base of and the number of layers.

The output will be layers as number of layers and x - sum as the count of remaining boxes.

Implementation

For sake of simplicity, we will be implementing the solution in Python.

x = int(input())

i = 1
sum = 0

layers = 0

while sum + i**2 <= x:
    layers += 1
    i += 1
    sum += i**2

print(layers)
print(x - sum)