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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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ave
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binary
balancing
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means
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proportion
scales
grids
symmetry
unit fractions
coordinates
medians
shape
percentages
sport
partitions
star numbers
cube numbers
even numbers
hexagons
2d shapes
digital products
logic
consecutive integers
circles
3d shapes
sums
powers
graphs
pentagons
triangle numbers
calculus
spheres
volume
squares
complex numbers
folding tube maps
functions
quadratics
crossnumbers
clocks
bases
determinants
indices
parabolas
decahedra
matrices
wordplay
integers
averages
expansions
cryptic crossnumbers
triangles
menace
gerrymandering
the only crossnumber
combinatorics
algebra
trigonometry
square numbers
chalkdust crossnumber
routes
range
chocolate
consecutive numbers
differentiation
tournaments
geometric mean
cards
digital clocks
polygons
factors
books
perimeter
dice
numbers grids
polynomials
addition
square grids
sets
time
planes
sequences
pascal's triangle
integration
cubics
dodecagons
square roots
money
odd numbers
tangents
dominos
remainders
rectangles
colouring
digits
people maths
area
neighbours
doubling
games
crosswords
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regular shapes
angles
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