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