# 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## Four points on a shape

Source: UKMT Senior Maths Challenge 2014

Fiona wants to draw a 2-dimensional shape whose perimeter passes through the points A, B, C and D

Which of the following shapes can she draw?

(i) A circle

(ii) An equilateral triangle

(iii) A square

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

## Fair dice

Source: Futility Closet

Timothy and Urban are playing a game with two six-sided dice. The dice are unusual: Rather than bearing a number, each face is painted either red or blue.

The two take turns throwing the dice. Timothy wins if the two top faces are the same color, and Urban wins if they're different. Their chances of winning are equal.

The first die has 5 red faces and 1 blue face. What are the colours on the second die?

## Half digits

Source: Maths Jam

Can you use each of the digits 1 to 9 to make a fraction which is equal to a half?

## Pizza

Twelve friends want to share a pizza. One of the friends is very fussy and will not eat the centre of the pizza.

Is it possible to split a (circular) pizza into twelve identical pieces such that there is at least one piece which does not touch the centre?

## Frogs

Source: nrich

Two frogs and two toads are standing on five lily pads.

The frogs and toads need to pass each other. They can only move by jumping one or two lily pads forward. In jumping two pads forwards they can jump over other frogs or toads.

How many jumps need to be made to get the frogs and toads past each other?