# 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

advent clocks ellipses algebra digits probability sport scales star numbers complex numbers lines partitions sums ave square numbers irreducible numbers rectangles means rugby integration symmetry coins speed routes angles graphs calculus cryptic crossnumbers prime numbers probabilty spheres crossnumbers perfect numbers palindromes triangles colouring coordinates division indices bases menace addition square roots multiples perimeter odd numbers cards people maths numbers crosswords sum to infinity chalkdust crossnumber percentages polygons triangle numbers averages area factors 3d shapes balancing functions sequences chess dodecagons factorials remainders multiplication number 2d shapes differentiation parabolas arrows money volume doubling proportion fractions floors surds trigonometry dice circles grids wordplay books christmas games shape taxicab geometry geometry hexagons unit fractions squares mean time pascal's triangle regular shapes shapes dates chocolate planes cube numbers logic quadratics integers folding tube maps cryptic clues## 19 December

Today's number is the number of 6-dimensional sides on a 8-dimensional hypercube.

## 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 \((x+y+z)^{16}\).

## 17 December

For \(x\) and \(y\) between 1 and 9 (including 1 and 9), I write a number at the co-ordinate \((x,y)\): if \(x\lt y\), I write \(x\); if not,
I write \(y\).

Today's number is the sum of the 81 numbers that I have written.

## 16 December

Arrange the digits 1-9 in a 3×3 square so that the first row makes a triangle number, the second row's digits are all even, the third row's digits are all odd; the first column makes a square number, and the second column makes a cube number.
The number in the third column is today's number.

triangle | |||

all digits even | |||

all digits odd | |||

square | cube | today's number |

## 15 December

Today's number is smallest three digit palindrome whose digits are all non-zero, and that is not divisible by any of its digits.

## 14 December

Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums are correct. The sums should be read left to right and top to bottom ignoring the usual order of operations. For example, 4+3×2 is 14, not 10. Today's number is the product of the numbers in the red boxes.

- | + | = 10 | |||

÷ | + | ÷ | |||

÷ | + | = 3 | |||

+ | - | ÷ | |||

+ | × | = 33 | |||

= 7 | = 3 | = 3 |

## 13 December

There is a row of 1000 lockers numbered from 1 to 1000. Locker 1 is closed and locked and the rest are open.

A queue of people each do the following (until all the lockers are closed):

- Close and lock the lowest numbered locker with an open door.
- Walk along the rest of the queue of lockers and change the state (open them if they're closed and close them if they're open) of all the lockers that are multiples of the locker they locked.

Today's number is the number of lockers that are locked at the end of the process.

Note: closed and locked are different states.

## 12 December

There are 2600 different ways to pick three vertices of a regular 26-sided shape. Sometime the three vertices you pick form a right angled triangle.

Today's number is the number of different ways to pick three vertices of a regular 26-sided shape so that the three vertices make a right angled triangle.