# Puzzles

## Archive

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#### Advent calendar 2018

#### Sunday Afternoon Maths LXVI

Cryptic crossnumber #2#### Sunday Afternoon Maths LXV

Cryptic crossnumber #1Breaking Chocolate

Square and cube endings

#### Sunday Afternoon Maths LXIV

Equal lengthsDigitless factor

Backwards fours

List of all puzzles

## Tags

regular shapes palindromes menace square roots dodecagons integration differentiation sums floors folding tube maps odd numbers complex numbers probability arrows crosswords trigonometry number integers perimeter sum to infinity circles grids crossnumbers books factorials dates pascal's triangle routes chocolate averages algebra numbers logic ave hexagons colouring cube numbers remainders fractions perfect numbers geometry digits coins multiplication indices percentages ellipses functions shape taxicab geometry addition advent irreducible numbers 3d shapes multiples proportion rectangles means 2d shapes christmas cards probabilty calculus polygons triangle numbers parabolas planes angles squares square numbers symmetry division star numbers shapes unit fractions mean people maths bases lines factors chess dice quadratics wordplay sequences spheres surds graphs cryptic crossnumbers volume speed chalkdust crossnumber games doubling sport rugby money partitions coordinates cryptic clues triangles clocks prime numbers time area## 6 December

\(p(x)\) 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 \(p(6)\)?

## Between quadratics

Source: Luciano Rila (@DrTrapezio)

\(p(x)\) is a quadratic polynomial with real coefficients. For all real numbers \(x\),

$$x^2-2x+2\leq p(x)\leq 2x^2-4x+3$$
\(p(11)=181\). Find \(p(16)\).

## Parabola

Source:

*Alex Through the Looking-Glass: How Life Reflects Numbers and Numbers Reflect Life*by Alex BellosOn a graph of \(y=x^2\), two lines are drawn at \(x=a\) and \(x=-b\) (for \(a,b>0\). The points where these lines intersect the parabola are connected.

What is the y-coordinate of the point where this line intersects the y-axis?

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**© Matthew Scroggs 2018**