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

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2019