mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

18 December

The expansion of \((x+y+z)^3\) is
$$x^3 + y^3 + z^3 + 3x^2y + 3x^2z + 3xy^2 + 3y^2z + 3xz^2 + 3yz^2 + 6xyz.$$
This has 10 terms.
Today's number is the number of terms in the expansion of \((x+y+z)^{26}\).

Show answer

Tags: algebra

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

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2020

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2021