# Puzzles

## Archive

Show me a random puzzle**Most recent collections**

#### Sunday Afternoon Maths LXVII

Coloured weightsNot Roman numerals

#### Advent calendar 2018

#### Sunday Afternoon Maths LXVI

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

Cryptic crossnumber #1Breaking Chocolate

Square and cube endings

List of all puzzles

## Tags

menace volume sequences odd numbers folding tube maps scales lines arrows multiples coins chess probabilty christmas dice complex numbers fractions numbers cards wordplay balancing routes cryptic crossnumbers bases 3d shapes hexagons digits proportion partitions differentiation circles perimeter money remainders logic addition trigonometry indices means triangles polygons crosswords chocolate floors dates perfect numbers integration functions calculus sum to infinity division books 2d shapes parabolas coordinates sport grids graphs games taxicab geometry shapes chalkdust crossnumber dodecagons spheres factorials clocks averages prime numbers time irreducible numbers rugby people maths multiplication mean ellipses ave quadratics probability speed squares rectangles integers doubling pascal's triangle crossnumbers planes number area square numbers surds regular shapes cube numbers algebra symmetry percentages triangle numbers geometry cryptic clues advent angles palindromes shape factors star numbers colouring unit fractions sums square roots## 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 2019**