mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

Archive

Show me a random puzzle
 Most recent collections 

Tags

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

Archive

Show me a random puzzle
▼ show ▼

18 December

There are 6 terms in the expansion of \((x+y+z)^2\):
$$(x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2xz$$
Today's number is number of terms in the expansion of \((x+y+z)^{16}\).

Show answer

Tags: algebra

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

Two tangents

Source: Reddit
Find a line which is tangent to the curve \(y=x^4-4x^3\) at 2 points.

Show answer

A bit of Spanish

Each of the letters P, O, C, M, U and H represent a different digit from 0 to 9.
Which digit does each letter represent?

Show answer & extension

Algebraic fractions

Given that
$$\frac{3x+y}{x-3y}=-1$$
what is the value of
$$\frac{x+3y}{3x-y}$$
?

Show answer & extension

Tags: algebra

Four integers

\(a\), \(b\), \(c\) and \(d\) are four positive (and non-zero) integers.
$$abcd+abc+bcd+cda+dab+ab+bc+cd+da+ac+bd\\+a+b+c+d=2009$$
What is the value of \(a+b+c+d\)?

Show answer & extension

Times roamin'

What is the product of this series?
$$(x-a)(x-b)(x-c)...(x-z)$$

Show answer

Tags: algebra
© Matthew Scroggs 2019