7-progressive-spiral-number-position.py

# Assume that you started to store items in progressively expanding square location,
# like this for the first 9 numbers:

# 05 04 03
# 06 01 02
# 07 08 09
# And like this for the expanding to include up to the first 25 numbers:

# 17 16 15 14 13
# 18 05 04 03 12
# 19 06 01 02 11
# 20 07 08 09 10
# 21 22 23 24 25

# You might easily notice that the first - and innermost - layer containes only 
# one number (01), the second one - immediately around it - contains 8 numbers 
# (number in the 02-09 range) and so on.

# Your task is to create a function that given a number n simply returns the number 
# of layers required to store up to n (included).

# layers(1) == 1
# layers(5) == 2
# layers(25) == 3
# layers(30) == 4
# layers(50) == 5

# Fair warning: you will always and only get positive integers, but be ready for 
# bigger numbers in the tests!


def layers(n):
    if n == 1:
        return 1
    elif n < 10:
        return 2
    else:
        Cont = True
        total, layer, addition = 9, 2, 8
        while Cont:
            addition += 8
            layer += 1 
            total += addition
            if total >= n:
                Cont = False
        return layer



print(layers(1))
print(layers(5))
print(layers(25))
print(layers(30))
print(layers(50))
print(layers(2951389217))

# Test.assert_equals(layers(1),1)
# Test.assert_equals(layers(5),2)
# Test.assert_equals(layers(25),3)
# Test.assert_equals(layers(30),4)
# Test.assert_equals(layers(50),5)