10 December

For all values of \(x\), the function \(f(x)=ax+b\) satisfies
$$8x-8-x^2\leqslant f(x)\leqslant x^2.$$
What is \(f(65)\)?
Edit: The left-hand quadratic originally said \(8-8x-x^2\). This was a typo and has now been corrected.

Show answer

10 December

The equation \(x^2+1512x+414720=0\) has two integer solutions.
Today's number is the number of (positive or negative) integers \(b\) such that \(x^2+bx+414720=0\) has two integer solutions.

Show answer

Powerful quadratics

Source: nrich
Find all real solutions to

Show answer


Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020