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Advent calendar 2017
6 December
All 2017 advent puzzles
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\(p(x)\) is a quadratic with real coefficients. For all real numbers \(x\),
$$x^2+4x+14\leq p(x)\leq 2x^2+8x+18$$
\(p(2)=34\). What is \(p(6)\)?
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106
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unit fractions
sport
integers
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elections
books
numbers
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christmas
squares
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algebra
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geometric mean
taxicab geometry
doubling
colouring
geometric means
mean
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division
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range
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tiling
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3d shapes
prime numbers
balancing
median
medians
combinatorics
palindromes
crosswords
probabilty
wordplay
hexagons
number
games
quadrilaterals
sums
addition
rugby
trigonometry
expansions
speed
cubics
rectangles
fractions
chocolate
decahedra
ave
geometry
consecutive numbers
neighbours
surds
even numbers
square grids
polygons
axes
integration
perimeter
routes
logic
quadratics
shapes
area
spheres
percentages
digital clocks
chalkdust crossnumber
determinants
crossnumbers
perfect numbers
odd numbers
sum to infinity
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