# Puzzles

## 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, Meg Reeny, Jo Ranger, and Fred Metcalfe—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.## 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.