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

7 December

The sum of the coefficients in the expansion of \((x+1)^5\) is 32. Today's number is the sum of the coefficients in the expansion of \((2x+1)^5\).

Show answer

Tags: algebra

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

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020