# 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

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

**
**

**© Matthew Scroggs 2019**