# Puzzles

## Archive

Show me a Random Puzzle**Most Recent Collections**

#### Sunday Afternoon Maths LVIII

Factorial PatternPlacing Plates

#### Advent Calendar 2016

#### Sunday Afternoon Maths LVII

Largest Odd FactorsSquare Factorials

#### Sunday Afternoon Maths LVI

An Arm and a LegList 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 rectangles clocks menace routes taxicab geometry remainders chalkdust crossnumber palindromes sequences means unit fractions division square roots surds doubling quadratics indices symmetry planes volume number partitions ave pascal's triangle mean advent## Factorial Pattern

$$1\times1!=2!-1$$ $$1\times1!+2\times2!=3!-1$$ $$1\times1!+2\times2!+3\times3!=4!-1$$Does this pattern continue?

## Placing Plates

Two players take turns placing identical plates on a square table. The player who is first to be unable to place a plate loses. Which player wins?

## Advent 2016 Murder Mystery

2016's Advent calendar ended with a murder mystery, with each of
the murderer, motive, weapon and location being a digit from 1 to 9.
Here are the clues:

10

None of the digits of

None of the digits of

**171**is the location.3

None of the digits of

None of the digits of

**798**is the motive.7

One of the digits of

One of the digits of

**691**is the location.16

None of the digits of

None of the digits of

**543**is the location.5

One of the digits of

One of the digits of

**414**is the murderer.20

The first digit of

The first digit of

**287**is the number of false red clues.8

Clues on days that are factors of

Clues on days that are factors of

**768**are all true.22

The murderer is the square root of one of the digits of

The murderer is the square root of one of the digits of

**191**.11

One of the digits of

One of the digits of

**811**is the weapon.19

The highest common factor of the weapon and

The highest common factor of the weapon and

**128**is 1.13

None of the digits of

None of the digits of

**512**is the murderer.18

One of the digits of

One of the digits of

**799**is the motive.17

None of the digits of

None of the digits of

**179**is the motive.6

None of the digits of

None of the digits of

**819**is the location.24

One of the digits of

One of the digits of

**319**is total number of false clues.23

One of the digits of

One of the digits of

**771**is the murderer.2

The weapon is not one of the digits of

The weapon is not one of the digits of

**435**.14

The final digit of

The final digit of

**415**is the number of true blue clues.4

The weapon is a factor of

The weapon is a factor of

**140**.12

The number of false clues before today is the first digit of

The number of false clues before today is the first digit of

**419**.9

One of the digits of

One of the digits of

**447**is the motive.1

None of the digits of

None of the digits of

**563**is the motive.21

One of the digits of

One of the digits of

**816**is the murderer.15

One of the digits of

One of the digits of

**387**is the motive.## 24 December

Today's number is 191 more than one of the other answers and
100 less than another of the answers.

## 23 December

Today's number is the number of three digit numbers that are not three more than a multiple of 7.

## 22 December

Today's number is a palindrome. Today's number is also the number of palindromes between 111 and 11111 (including 111 and 11111).

## 21 December

Today's number is a multiple of three. The average (mean) of all the answers that are multiples of three is a multiple of 193.

## 20 December

Earlier this year, I wrote a blog post about different ways to prove Pythagoras' theorem. Today's puzzle uses Pythagoras' theorem.

Start with a line of length 2. Draw a line of length 17 perpendicular to it. Connect the ends to make a right-angled triangle.
The length of the hypotenuse of this triangle will be a non-integer.

Draw a line of length 17 perpendicular to the hypotenuse and make another right-angled triangle. Again the new hypotenuse will have a non-integer length.
Repeat this until you get a hypotenuse of integer length. What is the length of this hypotenuse?