mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

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
$$(x^2-7x+11)^{(x^2-11x+30)}=1.$$

Show answer

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2020

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2021