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Advent calendar 2018
18 December
All 2018 advent puzzles
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There are 6 terms in the expansion of \((x+y+z)^2\):
$$(x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2xz$$
Today's number is number of terms in the expansion of \((x+y+z)^{16}\).
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153
In general, the expansion of \((x+y+z)^n\) will have \(\frac12n(n-1)\) terms.
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proportion
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prime numbers
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christmas
digital products
number
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sets
square roots
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numbers
grids
digital clocks
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taxicab geometry
pascal's triangle
elections
ave
routes
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percentages
factors
median
cube numbers
perfect numbers
people maths
tiling
averages
complex numbers
crossnumbers
integers
rectangles
volume
factorials
trigonometry
integration
tangents
decahedra
neighbours
cubics
the only crossnumber
parabolas
polygons
folding tube maps
colouring
prime factors
sums
cards
area
tournaments
chess
square numbers
doubling
chocolate
division
coordinates
dice
clocks
binary
lists
triangles
crosswords
surds
shape
partitions
shapes
regular shapes
books
consecutive integers
cryptic crossnumbers
arrows
determinants
differentiation
spheres
graphs
lines
games
combinatorics
mean
planes
matrices
range
advent
dodecagons
calculus
hexagons
rugby
probabilty
axes
consecutive numbers
3d shapes
products
odd numbers
dominos
2d shapes
geometry
star numbers
perimeter
indices
menace
multiplaction squares
balancing
fractions
polynomials
means
chalkdust crossnumber
coins
sum to infinity
functions
angles
powers
multiplication
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even numbers
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geometric mean
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