mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

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

Archive

Show me a random puzzle
 Most recent collections 

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2019