# 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

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