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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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averages
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graphs
chocolate
colouring
factors
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addition
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multiplication
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sum to infinity
ave
means
taxicab geometry
decahedra
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clocks
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square grids
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christmas
speed
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pascal's triangle
menace
rectangles
numbers
dates
polygons
unit fractions
complex numbers
shape
dodecagons
consecutive integers
hexagons
palindromes
surds
even numbers
differentiation
regular shapes
gerrymandering
arrows
multiples
tiling
scales
probabilty
axes
polynomials
money
medians
cryptic crossnumbers
functions
volume
rugby
shapes
triangles
partitions
perfect numbers
sums
the only crossnumber
binary
balancing
squares
books
dominos
expansions
games
spheres
square numbers
folding tube maps
2d shapes
advent
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tournaments
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neighbours
digital products
cube numbers
consecutive numbers
grids
geometric means
coordinates
division
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chalkdust crossnumber
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lines
fractions
products
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median
range
square roots
ellipses
planes
people maths
odd numbers
powers
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© Matthew Scroggs 2012–2025
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