@@ -60,8 +60,15 @@ def fill_triangle(int_range: tuple[int, int] = (1000, 9999)) -> list[int]:
6060
6161 """
6262
63- def triangle (n : int ) -> int :
64- return n * (n + 1 ) // 2
63+ def triangle (num : int ) -> int :
64+ """
65+ Gives the Nth triangle number.
66+ >>> triangle(2)
67+ 3
68+ >>> triangle(5)
69+ 15
70+ """
71+ return num * (num + 1 ) // 2
6572
6673 st , end = int_range
6774 arr = []
@@ -89,8 +96,15 @@ def fill_square(int_range: tuple[int, int] = (1000, 9999)) -> list[int]:
8996
9097 """
9198
92- def square (n : int ) -> int :
93- return n ** 2
99+ def square (num : int ) -> int :
100+ """
101+ Gives the Nth square number.
102+ >>> square(2)
103+ 4
104+ >>> square(5)
105+ 25
106+ """
107+ return num ** 2
94108
95109 st , end = int_range
96110 arr = []
@@ -118,8 +132,15 @@ def fill_pentagonal(int_range: tuple[int, int] = (1000, 9999)) -> list[int]:
118132
119133 """
120134
121- def pentagon (n : int ) -> int :
122- return n * (3 * n - 1 ) // 2
135+ def pentagon (num : int ) -> int :
136+ """
137+ Gives the Nth pentagon number.
138+ >>> pentagon(2)
139+ 5
140+ >>> pentagon(5)
141+ 35
142+ """
143+ return num * (3 * num - 1 ) // 2
123144
124145 st , end = int_range
125146 arr = []
@@ -147,8 +168,15 @@ def fill_hexagonal(int_range: tuple[int, int] = (1000, 9999)) -> list[int]:
147168
148169 """
149170
150- def hexagon (n : int ) -> int :
151- return n * (2 * n - 1 )
171+ def hexagon (num : int ) -> int :
172+ """
173+ Gives the Nth hexagon number.
174+ >>> hexagon(2)
175+ 6
176+ >>> hexagon(5)
177+ 45
178+ """
179+ return num * (2 * num - 1 )
152180
153181 st , end = int_range
154182 arr = []
@@ -176,8 +204,15 @@ def fill_heptagonal(int_range: tuple[int, int] = (1000, 9999)) -> list[int]:
176204
177205 """
178206
179- def heptagon (n : int ) -> int :
180- return n * (5 * n - 3 ) // 2
207+ def heptagon (num : int ) -> int :
208+ """
209+ Gives the Nth heptagon number.
210+ >>> heptagon(2)
211+ 7
212+ >>> heptagon(5)
213+ 55
214+ """
215+ return num * (5 * num - 3 ) // 2
181216
182217 st , end = int_range
183218 arr = []
@@ -206,8 +241,15 @@ def fill_octagonal(int_range: tuple[int, int] = (1000, 9999)) -> list[int]:
206241
207242 """
208243
209- def octagon (n : int ) -> int :
210- return n * (3 * n - 2 )
244+ def octagon (num : int ) -> int :
245+ """
246+ Gives the Nth octagon number.
247+ >>> octagon(2)
248+ 8
249+ >>> octagon(5)
250+ 65
251+ """
252+ return num * (3 * num - 2 )
211253
212254 st , end = int_range
213255 arr = []
@@ -224,7 +266,7 @@ def octagon(n: int) -> int:
224266 return arr
225267
226268
227- def check_cyclic (x : int , y : int ) -> bool :
269+ def check_cyclic (num1 : int , num2 : int ) -> bool :
228270 """
229271 This function checks if two 4 digit numbers are cyclic.
230272 For this problem we are only concerned with 4 digit numbers.
@@ -240,12 +282,12 @@ def check_cyclic(x: int, y: int) -> bool:
240282
241283 """
242284
243- if x < 1000 or y < 1000 :
285+ if num1 < 1000 or num2 < 1000 :
244286 raise ValueError ("Both integers must be greater than 999" )
245- if x > 9999 or y > 9999 :
287+ if num1 > 9999 or num2 > 9999 :
246288 raise ValueError ("Both integers must be less than 10000" )
247289
248- return (x % 100 ) == (y // 100 )
290+ return (num1 % 100 ) == (num2 // 100 )
249291
250292
251293def solution () -> int :
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