Puzzles
25 December
It's nearly Christmas and something terrible has happened: after years of gradual wear and tear, Santa's magic sleigh has fallen apart.
You need to help Santa build a new sleigh so that he can deliver presents before Christmas is ruined for everyone.
The magic sleigh was built from parts bought from magic factories all over the world, and only the exact combination of parts will be magic enough to let Santa deliver all
the world's presents on Christmas Eve—but it's been a long time since a magic sleigh was last built and no-one can remember exactly which combination of parts is needed.
You need to use the clues below to work out which parts to order to build a new magic sleigh. There are five parts that you need to order
(runners, a chassis, a present holder, a seat for Santa, and a front of the sleigh with reins). There are nine suppliers (numbered from 1 to 9) that Santa can order parts from.
10
The chassis should not be ordered from 918
The chassis should not be ordered from 712
One of the parts should be ordered from 28
The chassis should not be ordered from 49
The front should not be ordered from 51
The chassis should not be ordered from 67
Santa's seat should be ordered from 3, 5, or 46
The front should not be ordered from 814
One of the parts should be ordered from 413
The runners should not be ordered from a factor of 17520
Today's clue and the clue on 19 December are false4
The chassis should not be ordered from 52
The chassis should not be ordered from 15
The chassis should not be ordered from 324
Santa's seat should be ordered from 6, 7, or 517
The runners should be ordered from 511
The chassis should not be ordered from 421
One of the parts should be ordered from 83
The front should not be ordered from 119
Exactly 4 of the clues are false15
The chassis should not be ordered from 1, 2, or 823
The chassis should be ordered from 422
The chassis should be ordered from 416
One of the parts should be ordered from 110
The chassis should not be ordered from 918
The chassis should not be ordered from 712
One of the parts should be ordered from 28
The chassis should not be ordered from 49
The front should not be ordered from 51
The chassis should not be ordered from 67
Santa's seat should be ordered from 3, 5, or 46
The front should not be ordered from 814
One of the parts should be ordered from 413
The runners should not be ordered from a factor of 17520
Today's clue and the clue on 19 December are false4
The chassis should not be ordered from 52
The chassis should not be ordered from 15
The chassis should not be ordered from 324
Santa's seat should be ordered from 6, 7, or 517
The runners should be ordered from 511
The chassis should not be ordered from 421
One of the parts should be ordered from 83
The front should not be ordered from 119
Exactly 4 of the clues are false15
The chassis should not be ordered from 1, 2, or 823
The chassis should be ordered from 422
The chassis should be ordered from 416
One of the parts should be ordered from 1You can use this page to try ordering parts for a sleigh.
25 December
It's nearly Christmas and something terrible has happened: there's been a major malfunction in multiple machines in Santa's toy factory, and
not enough presents have been made. Santa has a backup warehouse full of wrapped presents that can be used in the case of severe emergency, but the warehouse is locked.
You need to help Santa work out the code to unlock the warehouse so that he can deliver the presents before Christmas is ruined for everyone.
The information needed to work out the code to the warehouse is known by Santa and his three most trusted elves: Santa is remembering a three-digit number,
and each elf is remembering a one-digit and a three-digit number. If Santa and the elves all agree that the emergency warehouse should be opened, they can work out the code for the door as follows:
- Santa tells his three-digit number to the first elf.
- The first elf subtracts her three-digit number then multiplies by her one-digit number. She tells her result to the second elf.
- The second elf subtracts his three-digit number then multiplies by his one-digit number. He tells his result to the third elf.
- The third elf subtracts their three-digit number then multiplies by their one-digit number. Their result is a five-digit number that is the code to unlock the warehouse.
But this year, there is a complication: the three elves are on a diplomatic mission to Mars to visit Martian Santa and cannot be contacted, so you need to piece together their
numbers from the clues they have left behind:
21
138 is an elf's 3-digit number.
11
The third elf's 1-digit number is not 2.
18
The first elf's 1-digit number is not 6.
1
144 is an elf's 3-digit number.
15
The third elf's 1-digit number is not 7.
23
The HCF of the first and third elves' 1-digit numbers is not 1, 2, or 8.
12
The second elf's 1-digit number is not 2, 8, or 1.
8
The third elf's 1-digit number is not a factor of 575.
17
The first elf's 1-digit number is not 9.
20
The third elf's 1-digit number is not 4.
7
The third elf's 1-digit number is not 1.
4
The third elf's 1-digit number is not 9.
6
990 is a multiple of an elf's 3-digit number.
3
The first elf's 1-digit number is not 7.
22
The HCF of 851 and the third elf's 3-digit number is 1.
14
The second elf's 1-digit number is not 6, 2, or 5.
24
Santa's number is 444.
9
The first elf's 1-digit number is not 5.
5
The second elf's 1-digit number is not 1, 7, or 9.
10
The second elf's 1-digit number is not 4, 9, or 5.
13
One of the digits of the second elf's 3-digit number is 9.
19
The HCF of 256 and the second elf's 3-digit number is 1.
2
The first elf's 1-digit number is not a factor of 202.
16
The first elf's 1-digit number is not 3.
21
138 is an elf's 3-digit number.
11
The third elf's 1-digit number is not 2.
18
The first elf's 1-digit number is not 6.
1
144 is an elf's 3-digit number.
15
The third elf's 1-digit number is not 7.
23
The HCF of the first and third elves' 1-digit numbers is not 1, 2, or 8.
12
The second elf's 1-digit number is not 2, 8, or 1.
8
The third elf's 1-digit number is not a factor of 575.
17
The first elf's 1-digit number is not 9.
20
The third elf's 1-digit number is not 4.
7
The third elf's 1-digit number is not 1.
4
The third elf's 1-digit number is not 9.
6
990 is a multiple of an elf's 3-digit number.
3
The first elf's 1-digit number is not 7.
22
The HCF of 851 and the third elf's 3-digit number is 1.
14
The second elf's 1-digit number is not 6, 2, or 5.
24
Santa's number is 444.
9
The first elf's 1-digit number is not 5.
5
The second elf's 1-digit number is not 1, 7, or 9.
10
The second elf's 1-digit number is not 4, 9, or 5.
13
One of the digits of the second elf's 3-digit number is 9.
19
The HCF of 256 and the second elf's 3-digit number is 1.
2
The first elf's 1-digit number is not a factor of 202.
16
The first elf's 1-digit number is not 3.
You can to open the door here.
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.
![](javascript:showlimage("asc_example.png"))
The ASC coordinates of this pair of flowers are 12.52.12.13.84.55 (click to enlarge).
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?