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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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mean
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cube numbers
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cryptic clues
even numbers
wordplay
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range
menace
arrows
median
grids
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tournaments
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factorials
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pentagons
geometry
integers
multiplication
crossnumbers
people maths
money
probability
floors
coordinates
elections
numbers
angles
integration
expansions
digital products
cryptic crossnumbers
square numbers
factors
gerrymandering
determinants
books
bases
ave
unit fractions
volume
pascal's triangle
decahedra
square roots
coins
consecutive integers
symmetry
combinatorics
polygons
rugby
averages
games
speed
time
parabolas
palindromes
shape
matrices
perimeter
graphs
advent
ellipses
consecutive numbers
dodecagons
digits
area
chess
chocolate
tiling
products
complex numbers
division
star numbers
means
functions
irreducible numbers
geometric means
cards
planes
3d shapes
logic
regular shapes
spheres
crossnumber
axes
dates
geometric mean
fractions
lines
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