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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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number
dice
pentagons
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medians
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planes
sport
axes
binary
circles
arrows
probabilty
means
taxicab geometry
dominos
books
cube numbers
digital products
shape
square roots
crossnumbers
combinatorics
triangle numbers
functions
dodecagons
regular shapes
differentiation
tangents
sets
graphs
coordinates
numbers
determinants
spheres
scales
people maths
chess
geometry
coins
indices
palindromes
logic
fractions
addition
hexagons
rugby
calculus
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clocks
tiling
square grids
lines
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consecutive integers
christmas
shapes
chalkdust crossnumber
unit fractions
grids
algebra
cryptic crossnumbers
sequences
geometric means
geometric mean
multiplaction squares
odd numbers
advent
partitions
median
tournaments
division
even numbers
factorials
gerrymandering
doubling
factors
multiplication
decahedra
products
sum to infinity
chocolate
the only crossnumber
integers
crosswords
time
square numbers
matrices
games
cryptic clues
surds
2d shapes
ellipses
prime numbers
cards
xor
routes
prime factors
elections
angles
multiples
money
parabolas
neighbours
lists
menace
averages
remainders
pascal's triangle
expansions
polynomials
complex numbers
polygons
dates
irreducible numbers
sums
probability
floors
quadratics
trigonometry
colouring
percentages
folding tube maps
range
perfect numbers
cubics
speed
ave
star numbers
rectangles
triangles
integration
digits
squares
bases
balancing
3d shapes
consecutive numbers
symmetry
volume
area
powers
proportion
© Matthew Scroggs 2012–2026
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