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