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# Puzzles

## 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.
The ASC coordinates of this pair of flowers are 12.52.12.13.84.55 (click to enlarge).
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?

2018's Advent calendar ended with a logic puzzle: It's nearly Christmas and something terrible has happened: one of Santa's five helpers—Jo Ranger, Fred Metcalfe, Kip Urples, Meg Reeny, 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."
15
Kip says: "The curling match lasted 323 mins."
24
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."
17
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"
7
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."
5
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."
20
Meg says: "Jo started skiing at 7:30."
4
Bob says: "I went for a 150 min ski."
13
Kip says: "Jo started skiing at 6:08."
22
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."
12
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."
10
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."
3
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."
18
Jo says: "I spent 153 mins solving maths puzzles."
2
Fred says: "I was solving maths puzzles for 172 mins."
11
Meg says: "I spent 108 mins solving maths puzzles with Bob."

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."
10
Orange hat says: "249 is my favourite number."
5
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."
23
Red shoes says: "Carol wants a factor of 120. I am yesterday's elf."
4
Blue shoes says: "495 is my favourite number."
15
Blue shoes says: "Carol lives at 9, 6 or 8."
22
Purple trousers says: "Carol wants a factor of 294."
11
White shirt says: "497 is my favourite number."
6
Pink shirt says: "Ben does not live at the last digit of 106."
9
Blue shoes says: "Ben lives at 5, 1 or 2."
20
Orange hat says: "Carol wants the first digit of 233."
1
Red shoes says: "Alex wants 1, 2 or 3."
24
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."
14
Pink shirt says: "One child lives at the first digit of 819."
3
White shirt says: "Alex lives at 2, 1 or 6."
18
Green hat says: "Ben wants 1, 5 or 4."
7
Green hat says: "Ben lives at 3, 4 or 3."
12
Grey trousers says: "Alex lives at 3, 1 or 5."
19
Purple trousers says: "Carol lives at 2, 6 or 8."
8
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."
2
Red shoes says: "Alex wants 1, 4 or 2."

## 23 December

In the song The Twelve Days of Christmas, how many presents have been given after 8 days?

## What's the star?

In the Christmas tree below, the rectangle, baubles, and the star at the top each contain a number. The square baubles contain square numbers; the triangle baubles contain triangle numbers; and the cube bauble contains a cube number.
The numbers in the rectangles (and the star) are equal to the sum of the numbers below them. For example, if the following numbers are filled in:
then you can deduce the following:
What is the number in the star at the top of this tree?

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 171 is the location.
3
None of the digits of 798 is the motive.
7
One of the digits of 691 is the location.
16
None of the digits of 543 is the location.
5
One of the digits of 414 is the murderer.
20
The first digit of 287 is the number of false red clues.
8
Clues on days that are factors of 768 are all true.
22
The murderer is the square root of one of the digits of 191.
11
One of the digits of 811 is the weapon.
19
The highest common factor of the weapon and 128 is 1.
13
None of the digits of 512 is the murderer.
18
One of the digits of 799 is the motive.
17
None of the digits of 179 is the motive.
6
None of the digits of 819 is the location.
24
One of the digits of 319 is total number of false clues.
23
One of the digits of 771 is the murderer.
2
The weapon is not one of the digits of 435.
14
The final digit of 415 is the number of true blue clues.
4
The weapon is a factor of 140.
12
The number of false clues before today is the first digit of 419.
9
One of the digits of 447 is the motive.
1
None of the digits of 563 is the motive.
21
One of the digits of 816 is the murderer.
15
One of the digits of 387 is the motive.

## Santa

Each of the letters D, A, Y, S, N, T, B, R and E represents a different non-zero digit. The following sum is true:
$$\begin{array}{cccccc} D&A&D&D&Y\\ B&E&A&R&D&+\\ \hline S&A&N&T&A \end{array}$$
This has a unique solution, but I haven't found a way to find the solution without brute force. This less insightful sum is also true with the same values of the letters (and should allow you to find the values of the letters using logic alone):
$$\begin{array}{ccccc} R&A&T&S\\ N&E&R&D&+\\ \hline S&A&N&E \end{array}$$

## Archive

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