mscroggs
.co.uk
mscroggs
.co.uk
blog
puzzles
academic
talks
contact
subscribe
↓ ☰ ↓
subscribe
Loading image...
Advent calendar 2022
14 December
All 2022 advent puzzles
~
More information
Holly draws a line of connected regular pentagons like this:
She continues the pattern until she has drawn 204 pentagons. The perimeter of each pentagon is 5. What is the perimeter of her line of pentagons?
Show answer
Hide answer
The two pentagons at the end of the pattern each contribute 4 units to the permimeter. The remaining 202 pentagons each contribute 3 units to the perimeter. This gives a total perimeter of 2×4+202×3=
614
.
Tags:
pentagons
Archive
Show me a random puzzle
Most recent collections
Advent calendar 2024
Advent calendar 2023
Advent calendar 2022
Advent calendar 2021
List of all puzzles
Tags
folding tube maps
scales
axes
sum to infinity
planes
sets
palindromes
albgebra
time
consecutive numbers
routes
decahedra
money
tournaments
speed
trigonometry
prime numbers
colouring
tiling
medians
cards
menace
shape
partitions
christmas
arrows
coordinates
geometric means
irreducible numbers
digits
means
median
dominos
crossnumbers
sums
balancing
probabilty
fractions
taxicab geometry
cryptic clues
triangle numbers
probability
even numbers
2d shapes
crosswords
star numbers
doubling
ave
gerrymandering
ellipses
averages
percentages
consecutive integers
numbers grids
square grids
coins
angles
spheres
cubics
chess
regular shapes
determinants
quadrilaterals
lines
odd numbers
area
3d shapes
symmetry
chalkdust crossnumber
factors
squares
functions
shapes
perimeter
proportion
integers
polynomials
clocks
dice
pascal's triangle
expansions
books
digital clocks
remainders
geometric mean
chocolate
elections
algebra
unit fractions
circles
digital products
rugby
triangles
numbers
integration
geometry
square numbers
hexagons
cube numbers
floors
rectangles
dodecagons
sequences
dates
division
pentagons
square roots
polygons
advent
mean
parabolas
logic
graphs
volume
combinatorics
binary
factorials
neighbours
powers
indices
complex numbers
perfect numbers
sport
addition
cryptic crossnumbers
quadratics
the only crossnumber
bases
range
multiples
multiplication
tangents
calculus
games
differentiation
number
surds
wordplay
matrices
products
people maths
grids
Archive
Show me a random puzzle
▼ show ▼
▲ hide ▲
Most recent collections
Advent calendar 2024
Advent calendar 2023
Advent calendar 2022
Advent calendar 2021
List of all puzzles
Tags
people maths
multiples
floors
rugby
ave
sport
square roots
multiplication
integration
gerrymandering
folding tube maps
tournaments
triangle numbers
dates
geometric mean
prime numbers
squares
planes
remainders
crossnumbers
axes
surds
proportion
elections
shapes
advent
circles
number
polynomials
means
differentiation
menace
fractions
dodecagons
percentages
integers
3d shapes
doubling
clocks
cubics
coins
geometric means
unit fractions
cube numbers
chalkdust crossnumber
routes
lines
sequences
coordinates
star numbers
digits
time
parabolas
albgebra
money
chocolate
calculus
dominos
trigonometry
averages
triangles
matrices
indices
consecutive numbers
decahedra
irreducible numbers
cards
cryptic clues
shape
products
complex numbers
neighbours
even numbers
division
rectangles
powers
books
graphs
games
numbers grids
medians
pascal's triangle
numbers
binary
range
digital clocks
volume
probabilty
scales
pentagons
square grids
taxicab geometry
addition
hexagons
ellipses
functions
perfect numbers
chess
colouring
arrows
2d shapes
regular shapes
quadratics
christmas
sets
combinatorics
tangents
logic
consecutive integers
speed
sum to infinity
bases
cryptic crossnumbers
balancing
determinants
grids
the only crossnumber
square numbers
polygons
factors
sums
median
odd numbers
perimeter
symmetry
factorials
angles
tiling
partitions
quadrilaterals
mean
palindromes
expansions
dice
algebra
area
geometry
spheres
digital products
crosswords
wordplay
probability
© Matthew Scroggs 2012–2025
![](javascript:showlimage("adv2022-pents.png"))
