The Math Wizard | The Architect

The Math Wizard loves precision. He doesn't like "half a potion" or "half a shelf".

Sometimes you need to round numbers down (floor) and sometimes up (ceil).

Floor and Ceiling

Imagine a room. The floor is at the bottom, the ceiling is at the top.

math.floor(3.9) -> 3 (Rounds down)
math.ceil(3.1) -> 4 (Rounds up)

import math

# Floor: Removing the decimal part (basically)
print(math.floor(5.99)) # 5

# Ceil: Going to the next integer
print(math.ceil(5.01))  # 6

Max Potions (Floor)

We have ingredients for 29 / 3 = 9.66 potions. Since we can't make 0.66 of a potion, we need to round down. Use math.floor().

Shelves Needed (Ceil)

If we have 8 potions and each shelf holds 4, we need 2 shelves. But what if we had 9 potions? Key math: max_potions / potions_per_shelf. Use math.ceil() to make sure we have enough space.

Why not just use round()? Because round(3.5) goes to 4, but round(3.4) goes to 3. Sometimes you forcing direction matters!

Suggested Solution

Expand

Solution:

import math

# Step 1: Floor (Round down)
potions = 29 / 3
print("Potions we can make: " + str(math.floor(potions))) # 9

# Step 2: Ceil (Round up)
shelves_needed = 9 / 4
print("Shelves needed: " + str(math.ceil(shelves_needed))) # 3

Advanced Tips

Want more? Click to expand

F. Precision Matters

In banking app, rounding wrong means losing money.
In navigation app, rounding wrong means crashing into a wall.
floor and ceil give you control over the direction of the error.