# Puzzles

## Archive

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

#### Sunday Afternoon Maths LXVI

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

Cryptic crossnumber #1Breaking Chocolate

Square and cube endings

#### Sunday Afternoon Maths LXIV

Equal lengthsDigitless factor

Backwards fours

#### Sunday Afternoon Maths LXIII

Is it equilateral?Cube multiples

List of all puzzles

## Tags

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

## x to the power of x again

Let \(y=x^{x^{x^{x^{...}}}}\) [\(x\) to the power of (\(x\) to the power of (\(x\) to the power of (\(x\) to the power of ...))) with an infinite number of \(x\)s]. What is \(\frac{dy}{dx}\)?

## x to the power of x

If \(x^{x^{x^{x^{...}}}}\) [\(x\) to the power of (\(x\) to the power of (\(x\) to the power of (\(x\) to the power of ...))) with an infinite number of \(x\)s] is equal to 2, what is the value of \(x\)?