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Advent calendar 2022
14 December
All 2022 advent puzzles
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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?
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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
.
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coins
area
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odd numbers
triangle numbers
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combinatorics
multiplication
parabolas
expansions
perimeter
shapes
tangents
christmas
quadratics
albgebra
star numbers
regular shapes
routes
clocks
dice
polygons
addition
angles
sequences
tiling
grids
factorials
even numbers
palindromes
dates
ellipses
ave
factors
consecutive integers
means
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speed
proportion
circles
trigonometry
indices
cryptic clues
unit fractions
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games
partitions
range
geometry
mean
arrows
number
averages
integers
complex numbers
gerrymandering
bases
crossnumbers
quadrilaterals
calculus
integration
balancing
taxicab geometry
numbers
remainders
wordplay
binary
rugby
time
pascal's triangle
sum to infinity
symmetry
graphs
division
geometric mean
pentagons
chalkdust crossnumber
powers
chess
sets
square roots
chocolate
cards
doubling
2d shapes
differentiation
prime numbers
3d shapes
sport
scales
axes
menace
crosswords
cube numbers
floors
digits
digital clocks
fractions
shape
matrices
square grids
perfect numbers
squares
algebra
polynomials
numbers grids
hexagons
lines
probability
volume
spheres
advent
colouring
cryptic crossnumbers
medians
multiples
triangles
irreducible numbers
determinants
sums
dodecagons
percentages
dominos
consecutive numbers
digital products
median
the only crossnumber
cubics
coordinates
folding tube maps
logic
products
planes
functions
geometric means
rectangles
decahedra
© Matthew Scroggs 2012–2025
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