# Puzzles

## 25 December

It's nearly Christmas and something terrible has happened: you've just landed in a town in the Arctic circle with a massive bag of letters for Santa, but
you've lost to instructions for how to get to Santa's house near the north pole.
You need to work out where he lives and deliver the letters to him before Christmas is ruined for everyone.

Due to magnetic compasses being hard to use near the north pole, you brought with you a special Advent compass. This compass has nine numbered directions.
Santa has given the residents of the town clues about a sequence of directions that will lead to his house;
but in order to keep his location secret from present thieves,
he gave each resident two clues: one clue is true, and one clue is false.

Here are the clues:

9

"The 4th digit is **4**.""The 8th digit is

**4**."

4

"The 3rd digit is **1**.""The 4th digit is

**7**."

10

"The 11th digit is a factor of **888**.""The 11th digit is a factor of 88."

13

"The 3rd digit is **1**.""The 4th digit is

**6**."

23

"The 10th digit is **4**.""The 10th digit is

**3**."

1

"The last digit is **1**,

**9**or

**5**.""The last digit is

**1**."

5

"The 3rd digit is **1**.""The 4th digit is

**3**."

16

"The 5th digit is **3**.""The 6th digit is

**3**."

11

"The sequence's length is **2**+

**1**+

**6**.""The sequence's length is

**2**×

**1**×

**6**."

12

"The 6th to 8th digits are **3**,

**3**,

**4**.""The 7th to 9th digits are

**3**,

**3**,

**4**."

2

"The 7th digit is **4**.""The 8th digit is

**4**."

21

"The 5th digit is **3**.""The 9th digit is

**9**."

22

"The 9th digit is **9**.""The 10th digit is

**4**."

17

"The 3rd digit is **1**.""The 4th digit is

**9**."

15

"The 2nd* digit is **7**.""The 1st digit is

**8**."

14

"The 1st digit is **7**.""The 2nd digit is

**7**."

7

"The last digit is not **5**.""The 4th digit is

**5**."

3

"The 11th digit is a factor of 10.""The 11th digit is a factor of **321**."

6

"The sequence's length is **1**+

**9**+

**2**.""The sequence's length is

**1**×

**9**×

**2**."

20

"The 5th digit is **3**.""The 5th digit is

**4**."

19

"**5**does not appear.""

**5**appears exactly once."

24

"The 3rd digit is **1**.""The 4th digit is

**8**."

25

✔18

"The 1st digit is **3**,

**7**or

**8**.""The sequence's length is prime."

8

"The 3rd digit is **1**.""The 4th digit is

**2**."

You can view the map here.

## 25 December

It's nearly Christmas and something terrible has happened: while out on a test flight, Santa's sled was damaged and Santa, Rudolph and Blitzen fell to the ground over the Advent Isles.
You need to find Santa and his reindeer before Christmas is ruined for everyone.

You have gathered one inhabitant of the four largest Advent Isles—Rum, Land, Moon and County—and they are going to give you a series of clues about where Santa and his reindeer landed.
However, one or more of the islanders you have gathered may have been involved in damaging Santa's sled and causing it to crash: any islander involved in this will lie to you to attempt to stop
you from finding Santa and his reindeer.
Once you are ready to search for Santa, Rudolph and Blitzen, you can find the map by following this link.

Each of the clues will be about Santa's, Rudolph's or Blitzen's positions in Advent Standard Coordinates (ASC): ASC are given by six two-digit numbers with dots inbetween, for example

**12.52.12.13.84.55**. For this example coordinate, the islanders will refer to (the first)**12**as the first coordinate,**52**as the second coordinate, (the second)**12**as the third coordinate,**13**as the fourth coordinate,**84**as the fifth coordinate, and**55**as the sixth coordinate.Here are the clues:

3

Rum says: "The product of all the digits in Blitzen's six coords is **432**."

21

Moon says: "Blitzen's fifth coord is **23**."

9

Moon says: "Blitzen's third coord is **23**."

1

Land says: "Santa's third coord ends in **3**,

**0**or

**1**."

2

Land says: "Santa's third coord ends in **2**,

**0**or

**3**."

4

Rum says: "Santa's second coord ends in **3**,

**4**or

**1**."

12

Rum says: "Rudolph's second and sixth coords are both **64**."

10

Rum says: "All six of Rudolph's coords are factors of **256**."

18

Moon says: "Santa's fourth and fifth coords are both **79**."

24

County says: "Santa's third coord ends in **3**,

**2**or

**1**."

22

Land says: "Santa's sixth coord is not **43**."

7

Rum says: "Santa's sixth coord is **43**."

23

County says: "One of the digits of Santa's third coord is **7**."

25

✔14

Land says: "Santa's third coord is **12**."

5

Rum says: "Santa's first coord is **36**."

15

Rum says: "Blitzen's first coord is **23**."

17

Rum says: "The first digit of Santa's third coord is **1**."

8

County says: "Santa's third coord shares a factor (≠1) with **270**."

6

County says: "Santa's second coord is **21**."

16

Land says: "Blitzen's second coord is **21**."

20

Moon says: "All six of Rudolph's coords are multiples of **8**."

11

Moon says: "The sum of Rudolph's six coords is **192**."

13

Moon says: "Santa's second coord is **21**or

**11**."

19

Moon says: "Blitzen's fourth and sixth coords are both **11**."

To find a point's ASC coordinates, split a map of the islands into a 9×9 grid, then number the rows and columns 1 to 9: the first two digits of ASC give the vertical then horizontal position of a square in this grid.
The next two digits then give a smaller square when this square is then itself split into a 9×9 grid, and so on. An example is show below.

You can view the map here.

## Coloured weights

You have six weights. Two of them are red, two are blue, two are green. One weight of each colour is heavier than the other; the three heavy weights all weigh the same, and the three lighter weights also weigh the same.

Using a scale twice, can you split the weights into two sets by weight?

## Advent 2018 Logic Puzzle

2018's Advent calendar ended with a logic puzzle: It's nearly Christmas and something terrible has happened: one of Santa's five helpers—Bob Luey, Kip Urples, Fred Metcalfe, Meg Reeny, and Jo Ranger—has stolen all the presents during the North Pole's annual Sevenstival. You need to find the culprit before Christmas is ruined for everyone.

Every year in late November, Santa is called away from the North Pole for a ten hour meeting in which a judgemental group of elders decide who has been good and who has been naughty. While Santa is away, it is traditional for his helpers celebrate Sevenstival.
Sevenstival gets in name from the requirement that every helper must take part in exactly seven activities during the celebration; this year's
available activities were billiards, curling, having lunch, solving maths puzzles, table tennis, skiing, chess, climbing and ice skating.

Each activity must be completed in one solid block: it is forbidden to spend some time doing an activity, take a break to do something else then return to the first activity.
This year's Sevenstival took place between 0:00 and 10:00 (North Pole standard time).

During this year's Sevenstival, one of Santa's helpers seven activities included stealing all the presents from Santa's workshop.
Santa's helpers have 24 pieces of information to give to you, but the culprit is going to lie about everything in an attempt to confuse you, so be careful who you trust.

Here are the clues:

1

Meg says: "Between

Meg says: "Between

**2:33**and curling, I played billiards with Jo."15

Kip says: "The curling match lasted

Kip says: "The curling match lasted

**323**mins."24

Fred says: "In total, Jo and Meg spent

Fred says: "In total, Jo and Meg spent

**1**hour and**57**mins having lunch."8

Meg says: "A total of

Meg says: "A total of

**691**mins were spent solving maths puzzles."17

Jo says: "I played table tennis with Fred and Meg for

Jo says: "I played table tennis with Fred and Meg for

**2**+**8**+**5**mins."23

Meg says: "

Meg says: "

**1:32**was during my 83 min ski"7

Meg says: "The number of mins the curling game lasted is a factor of

Meg says: "The number of mins the curling game lasted is a factor of

**969**."16

Jo says: "I started skiing with Bob, and finished before Bob at

Jo says: "I started skiing with Bob, and finished before Bob at

**8:45**."5

Jo says: "At

Jo says: "At

**4:45**, Fred, Bob, Kip and I started a curling match."14

Fred says: "I spent

Fred says: "I spent

**135**mins playing chess with Meg."20

Meg says: "Jo started skiing at

Meg says: "Jo started skiing at

**7:30**."4

Bob says: "I went for a

Bob says: "I went for a

**150**min ski."13

Kip says: "Jo started skiing at

Kip says: "Jo started skiing at

**6:08**."22

Fred says: "Bob, Kip and I finished lunch at

Fred says: "Bob, Kip and I finished lunch at

**3:30**."6

Bob says: "I played billiards with Kip from 0:00 until

Bob says: "I played billiards with Kip from 0:00 until

**1:21**."12

Fred says: "Between 3:30 and 4:45, there were

Fred says: "Between 3:30 and 4:45, there were

**3**people climbing."21

Fred says: "In total, Bob, Meg and I spent

Fred says: "In total, Bob, Meg and I spent

**269**mins ice skating."10

Meg says: "Between 0:00 and

Meg says: "Between 0:00 and

**1:10**, I was ice skating."19

Jo says: "At

Jo says: "At

**1:12**, Fred and I were both in the middle of maths puzzles."3

Jo says: "Straight after curling, I had a

Jo says: "Straight after curling, I had a

**108**min game of chess with Kip."9

Fred says: "At

Fred says: "At

**2:52**, I started having lunch with Bob and Kip."18

Jo says: "I spent

Jo says: "I spent

**153**mins solving maths puzzles."2

Fred says: "I was solving maths puzzles for

Fred says: "I was solving maths puzzles for

**172**mins."11

Meg says: "I spent

Meg says: "I spent

**108**mins solving maths puzzles with Bob."## Breaking Chocolate

You are given a bar of chocolate made up of 15 small blocks arranged in a 3×5 grid.

You want to snap the chocolate bar into 15 individual pieces. What is the fewest number of snaps that you need to break the bar? (One snap consists of picking up one piece of chocolate and snapping it into two pieces.)

## Advent 2017 logic puzzle

2017'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.