# Puzzles

## Archive

Show me a random puzzle**Most recent collections**

#### Sunday Afternoon Maths LXVII

Coloured weightsNot Roman numerals

#### Advent calendar 2018

#### Sunday Afternoon Maths LXVI

Cryptic crossnumber #2#### Sunday Afternoon Maths LXV

Cryptic crossnumber #1Breaking Chocolate

Square and cube endings

List of all puzzles

## Tags

quadratics averages geometry circles chocolate prime numbers chess grids symmetry proportion digits polygons sums surds doubling regular shapes crossnumbers logic probabilty number scales cube numbers wordplay crosswords triangle numbers coordinates books shape arrows triangles ave speed advent irreducible numbers volume square roots 2d shapes fractions integers sport rugby odd numbers functions colouring cryptic clues star numbers coins chalkdust crossnumber pascal's triangle complex numbers angles percentages indices probability dice sum to infinity division addition partitions perfect numbers square numbers sequences palindromes rectangles algebra shapes parabolas unit fractions factorials lines christmas clocks balancing factors floors ellipses menace dates perimeter differentiation squares multiples spheres time money area bases means folding tube maps multiplication mean 3d shapes routes taxicab geometry planes cryptic crossnumbers trigonometry games cards dodecagons numbers integration hexagons remainders calculus people maths graphs## 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 \((x+y+z)^{16}\).

## 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.

## A bit of Spanish

Source: Futility Closet

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?

## Algebraic fractions

Source: UKMT Senior Maths Challenge 2014

Given that

$$\frac{3x+y}{x-3y}=-1$$
what is the value of

$$\frac{x+3y}{3x-y}$$
?

## Four integers

Source: Teach Further Maths Blog

\(a\), \(b\), \(c\) 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 \(a+b+c+d\)?