# Puzzles

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#### Advent Calendar 2017

#### Sunday Afternoon Maths LXII

What's the Star?#### Sunday Afternoon Maths LXI

XYZ#### Sunday Afternoon Maths LX

Where is Evariste?Bending a Straw

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## 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 rectangles clocks menace routes taxicab geometry remainders chalkdust crossnumber palindromes sequences means unit fractions division square roots surds doubling quadratics indices planes volume number partitions ave pascal's triangle mean advent symmetry arrows addition cube numbers star numbers perfect numbers## Advent 2017 Logic Puzzle

2016's Advent calendar ended with a logic puzzle: It's nearly Christmas and something terrible has happened: Santa and his two elves have been cursed! The curse has led Santa to forget which present three childrenâ€”Alex, Ben and Carolâ€”want and where they live.

The elves can still remember everything about Alex, Ben and Carol, but the curse is causing them to lie. One of the elves will lie on even numbered days and tell the truth on odd numbered days; the other elf will lie on odd numbered days and tell the truth on even numbered days. As is common in elf culture, each elf wears the same coloured clothes every day.

Each child lives in a different place and wants a different present. (But a present may be equal to a home.) The homes and presents are each represented by a number from 1 to 9.

Here are the clues:

21

White shirt says: "Yesterday's elf lied: Carol wants

White shirt says: "Yesterday's elf lied: Carol wants

**4**,**9**or**6**."10

Orange hat says: "

Orange hat says: "

**249**is my favourite number."5

Red shoes says: "Alex lives at

Red shoes says: "Alex lives at

**1**,**9**or**6**."16

Blue shoes says: "I'm the same elf as yesterday. Ben wants

Blue shoes says: "I'm the same elf as yesterday. Ben wants

**5**,**7**or**0**."23

Red shoes says: "Carol wants a factor of

Red shoes says: "Carol wants a factor of

**120**. I am yesterday's elf."4

Blue shoes says: "

Blue shoes says: "

**495**is my favourite number."15

Blue shoes says: "Carol lives at

Blue shoes says: "Carol lives at

**9**,**6**or**8**."22

Purple trousers says: "Carol wants a factor of

Purple trousers says: "Carol wants a factor of

**294**."11

White shirt says: "

White shirt says: "

**497**is my favourite number."6

Pink shirt says: "Ben does not live at the last digit of

Pink shirt says: "Ben does not live at the last digit of

**106**."9

Blue shoes says: "Ben lives at

Blue shoes says: "Ben lives at

**5**,**1**or**2**."20

Orange hat says: "Carol wants the first digit of

Orange hat says: "Carol wants the first digit of

**233**."1

Red shoes says: "Alex wants

Red shoes says: "Alex wants

**1**,**2**or**3**."24

Green hat says: "The product of the six final presents and homes is

Green hat says: "The product of the six final presents and homes is

**960**."17

Grey trousers says: "Alex wants the first digit of

Grey trousers says: "Alex wants the first digit of

**194**."14

Pink shirt says: "One child lives at the first digit of

Pink shirt says: "One child lives at the first digit of

**819**."3

White shirt says: "Alex lives at

White shirt says: "Alex lives at

**2**,**1**or**6**."18

Green hat says: "Ben wants

Green hat says: "Ben wants

**1**,**5**or**4**."7

Green hat says: "Ben lives at

Green hat says: "Ben lives at

**3**,**4**or**3**."12

Grey trousers says: "Alex lives at

Grey trousers says: "Alex lives at

**3**,**1**or**5**."19

Purple trousers says: "Carol lives at

Purple trousers says: "Carol lives at

**2**,**6**or**8**."8

Red shoes says: "The digits of

Red shoes says: "The digits of

**529**are the toys the children want."13

Green hat says: "One child lives at the first digit of

Green hat says: "One child lives at the first digit of

**755**."2

Red shoes says: "Alex wants

Red shoes says: "Alex wants

**1**,**4**or**2**."## Turning Squares

Source: Futility Closet

Each square on a chessboard contains an arrow point up, down, left or right. You start in the bottom left square. Every second you move one square in the direction shown by the arrow in your square. Just after you move, the arrow on the square you moved from rotates 90° clockwise. If an arrow would take you off the edge of the board, you stay in that square (the arrow will still rotate).

You win the game if you reach the top right square of the chessboard. Can I design a starting arrangement of arrows that will prevent you from winning?

## 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.## Hat Check

Source: Futility Closet

Three logicians, A, B and C, are wearing hats. Each has a strictly positive integer written on it. The number on one of the hats is the sum of the numbers on the other two.

The logicians say:

A: I don't know the number on my hat.

B: The number on my hat is 15.

Which numbers are on hats A and C?

## The Self Referential Crossword

Source: Alex Bellos's Monday puzzle

Fill in the following crossnumber grid so that each clue describes the solution.

For example, if some clues read "TEN DS", "ONE X" and "THREE ES" then there will be ten Ds, one X and three Es in the completed grid. The entries in the crossword include the spaces.

## Shinro

Source: AMS Grad Blog

In the grid below, there are 12 holes hidden in the grid. Each of the arrows is pointing towards at least one hole. None of the arrows covers a hole.

For example, the arrow in the first row tells you that at least one of the last four squares in that row contains a hole.

Find the location of all 12 holes.

## Dice Maze

Source: Daily Telegraph, 30/05/2015

Each colour represents a different direction (up, down, left or right) and the number of dots on each die tells you how far to go. Starting at the middle die, following the directions correctly will cause you to visit every die exactly once.

Which die will you visit last on the journey?

## Whist

Messrs. Banker, Dentist, Apothecary and Scrivener played whist last night. (whist is a four player card game where partners sit opposite each other.) Each of these gentlemen is the namesake of another's vocation.

Last night, the apothecary partnered Mr. Apothecary; Mr. Banker's partner was the scrivener; on Mr. Scrivener's right sat the dentist.

Who sat on the banker's left?