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

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

Archive

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