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