Puzzles
25 December
It's nearly Christmas and something terrible has happened: a machine in Santa's toy factory has malfunctioned, and is unable to finish building all
the presents that Santa needs.
You need to help Santa work out how to fix the broken machine so that he can build the presents and deliver them before Christmas is ruined for everyone.
Inside the broken machine, there were five toy production units (TPUs) installed at sockets labelled A to E. During the malfunction, these TPUs were
so heavily damaged that Santa is unable to identify which TPU they were when trying to fix the machine. The company that supplies TPUs builds 10 different units, numbered from 0 to 9.
You need to work out which of the 10 TPUs needs to be installed in each of the machine's sockets, so that Santa can fix the machine. It may be that two or more of the TPUs are the same.
21
C is not 2.
11
E is not 0.
18
One or more of the TPUs is 1
1
C is 1, 8, or 0.
15
C is 4, 4, or 4.
23
The clues on day 9 and day 23 are false.
12
Exactly 2 of the TPUs is/are even.
8
Exactly two of the TPUs are 2.
17
A is 2 and B is 2.
20
Exactly 4 of the TPUs is/are even.
7
D is 9, 8, or 7.
4
E is 2 or 6.
6
E is 2, 3, or 3.
3
A is 5.
22
E is not 7.
14
C is not 3, 9, or 9.
24
Strictly less than 10 clues are true.
9
The clues on days that are factors of 600 are false.
5
D is 3, 7, or 8.
10
C is 5.
13
E is not 8+1.
19
E is not 5 or 4
2
C is 6, 8, or 1.
16
A is 2 and B is 1.
You can attempt to fix the machine here.
Advent 2022 logic puzzle
It's nearly Christmas and something terrible has happened: an evil Christmas-hater has set three drones loose above Santa's stables. As long as the drones are flying around, Santa is unable to
take off to deliver presents to children all over the world.
You need to help Santa by destroying the drones so that he can deliver presents before Christmas is ruined for everyone.
Each of the three drones was programmed with four integers between 1 and 20 (inclusive): the first two of these are the drone's starting position; the last two give the drone's daily speed.
The drones have divided the sky above Santa's stables into a 20 by 20 grid. On 1 December, the drones will be at their starting position.
Each day, every drone will add the first number in their daily speed to their horizontal position, and the second
number to their vertical position. If the drone's position in either direction becomes greater than 20, the drone will subtract 20 from their position in that direction.
Midnight in Santa's special Advent timezone is at 5am GMT, and so the day will change and the drones will all move at 5am GMT.
For example, if a drone's starting position was (1, 12) and its movement was (5, 7), then:
- on day 1, it would be at (1, 12);
- on day 2, it would be at (6, 19);
- on day 3, it would be at (11, 6);
- on day 4, it would be at (16, 13);
- on day 5, it would be at (1, 20);
- on day 6, it would be at (6, 7);
- and so on.
You need to calculate each drone's starting position and daily speed, then work out where the drone currently is so you can shoot it down.
3
Blue's horizontal speed is not 3, 6, or 9.
14
On 4 December, blue's vertical position was 14.
15
Blue's vertical speed is not divisible by 2.
9
On 5 December, orange's vertical position was not 6.
2
Red's horizontal speed is a factor of 840.
6
Red's horizontal speed is not a factor of 128.
5
Blue's vertical speed is not 3, 1, or 5.
1
Red's vertical speed is 1.
12
Orange's horizontal speed is 1, 4, or 3.
24
The highest common factor of blue's horizontal speed and 28 is 1.
18
On 15 December, the horizontal position of one drone was 7.
8
Blue's vertical speed is a factor of 840.
11
Red's horizontal speed is 9, 8, or 7.
4
On 2 December, red's horizontal position was 5
16
Orange's horizontal speed is 3, 2, or 4.
22
Blue's horizontal speed is not a factor of 323.
10
On 8 December, the vertical position of two drones was 20.
19
On 16 December, the horizontal position of one drone was 8.
17
On 14 December, the horizontal position of one drone was 4.
21
Orange's horizontal speed is 2, 3, or 1.
13
On 6 December, the vertical position of two drones was 4.
20
Blue's horizontal speed is not 4, 2, or 5.
23
Blue's horizontal speed is 1 more or 1 less than a multiple of 5.
7
Blue's vertical speed is not 4, 7, or 6.
You can attempt to shoot down the drones here.
Advent 2021 logic puzzle
It's nearly Christmas and something terrible has happened: a saboteur has infiltrated the stables where Santa's reindeer are kept, and has caused all three of Santa's test flights to be unsuccessful.
You need to help Santa have a successful test flight so that he can deliver presents before Christmas is ruined for everyone.
In order to have enough magical power to fly with the sleigh, all nine of Santa's reindeer must be fed their favourite food. The saboteur gave one or more reindeer the wrong food before each of
the three test flights, causing the reindeer to be unable to take off.
In each clue, "before test flight n" means "immediately before test flight n". Before each test flight, each reindeer was fed exactly one
food, and two or more reindeer may have been fed the same food. Two or more reindeer may have the same favourite food. You must use these clues to work out what each reindeer's favourite food is, then complete a test flight by feeding each reindeer the correct food.
11
Before test flight 2, reindeer 9 was given food 5.
18
Before test flight 2, reindeer 8 was given food 2
2
Before test flight 1, reindeer 2 was given food 4.
9
Before test flight 1, 2 reindeer were given the wrong food.
10
Before test flight 1, reindeer 9 was given food 6
12
Before test flight 3, reindeer 9 was given food 1
19
Before test flight 3, reindeer 5 was not given food 7
21
Before test flight 3, reindeer 7 was given food that is a factor of 148
3
Before test flight 2, reindeer 2 was given food 4.
4
Before test flight 3, reindeer 2 was given food 6.
6
Reindeer 4's favourite food is a factor of 607
13
Before test flight 2, reindeer 4 was not given food 9
20
Before test flight 3, 3 reindeer had the food equal to their number
22
Before test flight 3, reindeer 7 was not given food 1
23
Before test flight 3, no reindeer was given food 2
5
Before test flight 3, 4 reindeer were given the wrong food.
7
Reindeer 4 was given the same food before all three test flights.
14
Before test flight 2, 2 reindeer were given the wrong food
16
Before test flight 2, all the reindeer were given different foods
17
Before test flight 1, reindeer 7 was not given food 7
24
Before test flight 1, reindeer 7 was not given food 9
1
Reindeer 2's favourite food is 4
8
Before test flight 1, reindeer 8 was given food 3.
15
Reindeer 1 was given food 1 before all three test flights
You can attempt a test flight here.
Advent 2020 logic puzzle
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.
Advent 2019 logic puzzle
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.
6 December
Noel's grandchildren were in born in November in consecutive years. Each year for Christmas, Noel gives each of his grandchildren their age in pounds.
Last year, Noel gave his grandchildren a total of £208. How much will he give them in total this year?
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—Fred Metcalfe, Kip Urples, Meg Reeny, Jo Ranger, and Bob Luey—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 2:33 and curling, I played billiards with Jo."
Meg says: "Between 2:33 and curling, I played billiards with Jo."
15
Kip says: "The curling match lasted 323 mins."
Kip says: "The curling match lasted 323 mins."
24
Fred says: "In total, Jo and Meg spent 1 hour and 57 mins having lunch."
Fred says: "In total, Jo and Meg spent 1 hour and 57 mins having lunch."
8
Meg says: "A total of 691 mins were spent solving maths puzzles."
Meg says: "A total of 691 mins were spent solving maths puzzles."
17
Jo says: "I played table tennis with Fred and Meg for 2+8+5 mins."
Jo says: "I played table tennis with Fred and Meg for 2+8+5 mins."
23
Meg says: "1:32 was during my 83 min ski"
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 969."
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 8:45."
Jo says: "I started skiing with Bob, and finished before Bob at 8:45."
5
Jo says: "At 4:45, Fred, Bob, Kip and I started a curling match."
Jo says: "At 4:45, Fred, Bob, Kip and I started a curling match."
14
Fred says: "I spent 135 mins playing chess with Meg."
Fred says: "I spent 135 mins playing chess with Meg."
20
Meg says: "Jo started skiing at 7:30."
Meg says: "Jo started skiing at 7:30."
4
Bob says: "I went for a 150 min ski."
Bob says: "I went for a 150 min ski."
13
Kip says: "Jo started skiing at 6:08."
Kip says: "Jo started skiing at 6:08."
22
Fred says: "Bob, Kip and I finished lunch at 3:30."
Fred says: "Bob, Kip and I finished lunch at 3:30."
6
Bob says: "I played billiards with Kip from 0:00 until 1:21."
Bob says: "I played billiards with Kip from 0:00 until 1:21."
12
Fred says: "Between 3:30 and 4:45, there were 3 people climbing."
Fred says: "Between 3:30 and 4:45, there were 3 people climbing."
21
Fred says: "In total, Bob, Meg and I spent 269 mins ice skating."
Fred says: "In total, Bob, Meg and I spent 269 mins ice skating."
10
Meg says: "Between 0:00 and 1:10, I was ice skating."
Meg says: "Between 0:00 and 1:10, I was ice skating."
19
Jo says: "At 1:12, Fred and I were both in the middle of maths puzzles."
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 108 min game of chess with Kip."
Jo says: "Straight after curling, I had a 108 min game of chess with Kip."
9
Fred says: "At 2:52, I started having lunch with Bob and Kip."
Fred says: "At 2:52, I started having lunch with Bob and Kip."
18
Jo says: "I spent 153 mins solving maths puzzles."
Jo says: "I spent 153 mins solving maths puzzles."
2
Fred says: "I was solving maths puzzles for 172 mins."
Fred says: "I was solving maths puzzles for 172 mins."
11
Meg says: "I spent 108 mins solving maths puzzles with Bob."
Meg says: "I spent 108 mins solving maths puzzles with Bob."
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 children—Alex, Ben and Carol—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 4, 9 or 6."
White shirt says: "Yesterday's elf lied: Carol wants 4, 9 or 6."
10
Orange hat says: "249 is my favourite number."
Orange hat says: "249 is my favourite number."
5
Red shoes says: "Alex lives at 1, 9 or 6."
Red shoes says: "Alex lives at 1, 9 or 6."
16
Blue shoes says: "I'm the same elf as yesterday. Ben wants 5, 7 or 0."
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 120. I am yesterday's elf."
Red shoes says: "Carol wants a factor of 120. I am yesterday's elf."
4
Blue shoes says: "495 is my favourite number."
Blue shoes says: "495 is my favourite number."
15
Blue shoes says: "Carol lives at 9, 6 or 8."
Blue shoes says: "Carol lives at 9, 6 or 8."
22
Purple trousers says: "Carol wants a factor of 294."
Purple trousers says: "Carol wants a factor of 294."
11
White shirt says: "497 is my favourite number."
White shirt says: "497 is my favourite number."
6
Pink shirt says: "Ben does not live at the last digit of 106."
Pink shirt says: "Ben does not live at the last digit of 106."
9
Blue shoes says: "Ben lives at 5, 1 or 2."
Blue shoes says: "Ben lives at 5, 1 or 2."
20
Orange hat says: "Carol wants the first digit of 233."
Orange hat says: "Carol wants the first digit of 233."
1
Red shoes says: "Alex wants 1, 2 or 3."
Red shoes says: "Alex wants 1, 2 or 3."
24
Green hat says: "The product of the six final presents and homes is 960."
Green hat says: "The product of the six final presents and homes is 960."
17
Grey trousers says: "Alex wants the first digit of 194."
Grey trousers says: "Alex wants the first digit of 194."
14
Pink shirt says: "One child lives at the first digit of 819."
Pink shirt says: "One child lives at the first digit of 819."
3
White shirt says: "Alex lives at 2, 1 or 6."
White shirt says: "Alex lives at 2, 1 or 6."
18
Green hat says: "Ben wants 1, 5 or 4."
Green hat says: "Ben wants 1, 5 or 4."
7
Green hat says: "Ben lives at 3, 4 or 3."
Green hat says: "Ben lives at 3, 4 or 3."
12
Grey trousers says: "Alex lives at 3, 1 or 5."
Grey trousers says: "Alex lives at 3, 1 or 5."
19
Purple trousers says: "Carol lives at 2, 6 or 8."
Purple trousers says: "Carol lives at 2, 6 or 8."
8
Red shoes says: "The digits of 529 are the toys the children want."
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 755."
Green hat says: "One child lives at the first digit of 755."
2
Red shoes says: "Alex wants 1, 4 or 2."
Red shoes says: "Alex wants 1, 4 or 2."