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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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gerrymandering
3d shapes
volume
differentiation
tiling
christmas
chess
lines
money
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square grids
symmetry
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rugby
numbers grids
digital products
expansions
unit fractions
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squares
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factors
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irreducible numbers
people maths
powers
menace
prime numbers
numbers
bases
tournaments
wordplay
binary
graphs
even numbers
cards
products
circles
scales
shape
cubics
planes
matrices
sums
perfect numbers
elections
quadrilaterals
pascal's triangle
multiples
advent
median
coins
books
geometric means
colouring
coordinates
sum to infinity
odd numbers
sets
games
albgebra
clocks
range
integration
perimeter
consecutive integers
probability
geometry
percentages
folding tube maps
axes
balancing
pentagons
2d shapes
regular shapes
rectangles
spheres
polynomials
tangents
square numbers
grids
proportion
chalkdust crossnumber
hexagons
taxicab geometry
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sport
floors
factorials
logic
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dice
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square roots
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