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

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

Archive

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