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Welcome to 2022 everyone! Now that the Advent calendar has disappeared, it's time to reveal the answers and annouce the winners. But first, some good news: with your help, a successful test flight was made and Christmas was saved!

Now that the competition is over, the questions and all the answers can be found here. Before announcing the winners, I'm going to go through some of my favourite puzzles from the calendar, reveal the solution and a couple of other interesting bits and pieces.

My first highlight is the puzzle from 2 December. I like this puzzle, as it's very difficult (maybe impossible) to work out by brute force (as \(n\) is a huge number), and the solution method I used was satisfying.

My next hightlight is the puzzle from 5 December. It's difficult to find many triangles with perimeter 50 and an integer area, but there's a neat way to solve this without needing to find any.

My next highlight is the puzzle from 14 December. This is closely related to the puzzle from 12 December but this time movements to the left are allowed. I enjoyed a nice "aha!" moment when designing this puzzle.

My final highlight is the puzzle from 16 December. If you enjoyed this one, you'll probably also enjoy the crossnumber I wrote for Chalkdust issue 13.

Once you've entered 24 answers, the calendar checks these and tells you how many are correct. I logged the answers that were sent for checking and have looked at these to see which puzzles were the most and least commonly incorrect. The bar chart below shows the total number of incorrect attempts at each question.

You can see that the most difficult puzzles were those on 5 and 14 December; and the easiest puzzles were on 6, 8, and 9 December.

The numbers on the doors of the Advent calendar formed a magic square: the numbers in each row, each column, and on the two major diagonals all add up to the same total.

This was spotted by both Colin Beveridge (@icecolbeveridge) and Alex on 15 December.

And finally (and maybe most importantly), on to the winners: 150 people solved all the puzzles and made a successful test flight. That's down on last year but up on two years ago:

From the correct answers, the following 10 winners were selected:

Congratulations! Your prizes will be on their way shortly.

The prizes this year include 2021 Advent calendar T-shirts. If you didn't win one, but would like one of these, I've made them available to buy at merch.mscroggs.co.uk alongside the T-shirts from previous years.

Additionally, well done to Aaron Stiff, Alan Buck, Alanis, Alek2ander, Alex, Alex Davis, Andrew Brady, Andrew Roy, Andrew Turner, Austin, B Moreland, Becky Russell, Ben Baker, Ben Boxall, Ben Jones, Ben Reiniger, Ben Tozer, Berl Steiner, Brennan Dolson, Brian Carnes, Brian Wellington, Carl Westerlund, Carmen, Cathy Hooper, Chris Hellings, Christopher Adams, Christy Hales, Connie, Corbin Groothuis, CreativeCrocheter, Dan DiMillo, Dan Whitman, Daniel Chiverton, Daniel Low, Dave Budd, David Ault, David Berardo, David Fox, David Kendel, David Mitchell, David P, David and Ivy Walbert, Deborah Tayler, Dylan Madisetti, Elijah Kuhn, Emily Troyer, Eric, Eric Kolbusz, Erik Eklund, Frank Kasell, Franklin Ta, Fred Verheul, Gabriella Pinter, Gary M. Gerken, Gert-Jan de Vries, Gregory Loges, Gwendolenn, Hannah , Harry Allen, Heerpal Sahota, Helen, Helen Bradley, Håkon Balteskard, Iris, Jacob Y, James Chapman, Jarvis, Jay Miller, Jean-Noël Monette, Jean-Sébastien Turcotte, Joe Gage, John Alasdair Warwicker, Jon Palin, Jonathan Chaffer, Jonathan Winfield, Jorge del Castillo, Joseph Wagner, Kai, Karen Climis, Kim Brooks, Kristen Koenigs, Lauren Woolsey, Lemminkäinen, Lewis Dyer, Liz Madisetti, Louis, Luke S, Maggie Orr, Magnus Eklund, Marco van der Park, Maria, Mark Stambaugh, Martin Harris, Martin Holtham, Matt Askins, Matthew, Matthew Schulz, Mels, Michael DeLyser, Mihai Zsisku, Mike Hands, Millie, NIck C, Nadine Chaurand, Naomi Bowler, Nick Keith, Niji, Nikos I., Noah Overcash, Oscar, Friend of Rudolph, patrick fussell, Ray Arndorfer, Rea, Reuben Cheung, Riccardo Lani, Rick Simineo, Robert Brady, Roger Lipsett, Rosie Paterson, Russ Collins, Ruth, Ryan W, Scott, Sean Carmody, Sean Henderson, Seth Cohen, SherlockSage, Simon Schneider, Tamara Brenner, Tarim, Tom Fryers, Tony Mann, tripleboleo, Tristan S, UsrBinPRL, Valentin VĂLCIU, Vinayak, Yasha, Yuliya Nesterova, and Yurie Ito, who all also completed the Advent calendar but were too unlucky to win prizes this time or chose to not enter the prize draw.

See you all next December, when the Advent calendar will return.

This year, the front page of mscroggs.co.uk will once again feature an Advent calendar, just like in each of the last six years. Behind each door, there will be a puzzle with a three digit solution. The solution to each day's puzzle forms part of a 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.

Behind each day (except Christmas Day), there is a puzzle with a three-digit answer. Each of these answers forms part of a piece of information about the reindeer's favourite foods and what the reindeer were fed before the three test flights. 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.

You can use this page to attempt up to three test flights per day. An attempted test flight will be successful if and only if all nine reindeer are given their favourite food just before the flight.

Ten randomly selected people who solve all the puzzles, complete a successful test flight, and fill in the entry form behind the door on the 25th will win prizes!

The prizes will include an mscroggs.co.uk Advent 2021 T-shirt. If you'd like one of the T-shirts from a previous Advent, they are available to order at merch.mscroggs.co.uk.

The winners will be randomly chosen from all those who submit the entry form before the end of 2021. Each day's puzzle (and the entry form on Christmas Day) will be available from 5:00am GMT. But as the winners will be selected randomly, there's no need to get up at 5am on Christmas Day to enter!

As you solve the puzzles, your answers will be stored. To share your stored answers between multiple devices, enter your email address below the calendar and you will be emailed a magic link to visit on your other devices.

To win a prize, you must submit your entry before the end of 2021. Only one entry will be accepted per person. If you have any questions, ask them in the comments below or on Twitter.

So once December is here, get solving! Good luck and have a very merry Christmas!

It's 2021, and the Advent calendar has disappeared, so it's time to reveal the answers and annouce the winners. But first, some good news: with your help, Santa received all his letters and Christmas was saved!

Now that the competition is over, the questions and all the answers can be found here. Before announcing the winners, I'm going to go through some of my favourite puzzles from the calendar, reveal the solution and a couple of other interesting bits and pieces.

My first highlight is this puzzle from 5 December, that I think doesn't seem obvious that there's even a unique answer until you spot some nice properties of dice.

My next highlight is the puzzle from 15 December. I had a lot of fun trying to write this one. At the end, I tell you that T represents 4: this puzzle still has a unique answer without this, but it was too hard to get started.

My next highlight is the puzzle from 16 December. I had a lot of fun writing this one too. At least a few people seem to have enjoyed solving it, as indicated by this comment.

My final highlight is the puzzle from 21 December. My method for solving this one was quite complicated. Let me know in the comments or on Twitter if you have a better way of solving it.

Once you've entered 24 answers, the calendar checks these and tells you how many are correct. I logged the answers that were sent for checking and have looked at these to see which puzzles were the most and least commonly incorrect. The bar chart below shows the total number of incorrect attempts at each question.

You can see that the most difficult puzzles were those on 6, 14, 19, 21, and 24 December; and the easiest puzzles were on 3, 9, 10, 16, and 17 December.

The solutions to all the individual puzzles can be found here. If you want to read some alternative solutions to the puzzles, you can find Alira's solutions here, including a very nice explanation of how the final clues fit together to find the directions to Santa's house.

Using the daily clues, it was possible to work out that Santa's house could be found by following the directions 3,7,1,1,4,3,3,4,9,3,3,9 on this map.

Due to the way the Advent compass worked, there are actually a few different ways to get to Santa's house. For example, 7,5,7,1,1,4,3,3,4,9,3,3 also gets you there:

I'll leave you to work out how many different ways there are to get there...

Here's the full collection of tiles that you could find by walking around the map:

And finally (and maybe most importantly), on to the winners: 223 people found Santa's house entered the competition. This is quite a lot more than in previous years:

From the correct answers, the following 10 winners were selected:

Congratulations! Your prizes will be on their way shortly.

The prizes this year include 2020 Advent calendar T-shirts. If you didn't win one, but would like one of these, I've made them available to buy at merch.mscroggs.co.uk alongside the T-shirts from previous years.

Additionally, well done to 4nder, Ashley Frazer Jarvis, Aaron Stiff, Alan Buck, Alejandro Villarreal, Alex Bolton, Alex Davis, Alex Klapheke, Alexander Rakitin, Anders Kaseorg, Andrew, Andrew P Turner, Andy Ennaco, Annabel, Anthony Della Pella, Artie Smith, Athena, Austin, Austin Shapiro, Beau Ferguson, Becky Russell, Ben Buchwald, Ben Jones, Ben Reiniger, Benjamin Tozer, Bennet, Beth Jensen, Blake, Brennan Dolson, Brian Carnes, Brian Wellington, Burak Kadron, Caleb Likely, Callum Hobbis, Carl Westerlund, Carmen Günther, Cath Simpson, Cathy Hooper, Chris Hellings, Christy Hales, Colin, Colin Brockley, Connie, Corbin Groothuis, Cory Peters, Cosmo Viola, Dan Colestock, Dan DiMillo, Dan McIntyre, Dan Whitman, Dana Sussman, Daniel De la Paz, David, David Ault, David Berardo, David Fox, David Kendel, David Mitchell, David Parmenter, David and Ivy Walbert, Dean Thomas, Deborah Tayler, Don Anderson, Donagh Collins, Elizabeth Blackwell, Emilie Heidenreich, Emily Troyer, Eric Kolbusz, Eric Skoglund, Erik Eklund, Eva, Evan Louis Robinson, Fionn Woodcock, Frances Haigh, Frank Kasell, Franklin Ta, Fred Verheul, Georges, Gabriella Pinter, Gert-Jan de Vries, Graham Greve, Gregory Loges, Gwendal Collet, Harry Allen, Heerpal Sahota, Helen, Helen Matthews, Herschel Pecker, Håkon Balteskard, Ivan Arribas, Jacob Young, James Demers, James Laver, Jan, Jason Demers, Jason Kass, Jean-Sébastien Turcotte, Jeff Rubin, Jefff Michael, Jen Huang, Jessica Marsh, Jim Rogers, Joe Gage, Johan Asplund, John Alasdair Warwicker, Jon Foster, Jon Lipscombe, Jon Palin, Jonathan Chaffer, Jonathan Forsythe, Jonathan Winfield, Jordan Susskind, Jorge del Castillo, Kai Lam, Karen Climis, Keith Pound, Ken Cheung, Killeen, Kristen Koenigs, Kristin Gramza, Kurt Engleman, Laura Midgley, Lauren Woolsey, Lewis Dyer, Linus Banghart-Linn, Liz Madisetti, Louis de Mendonca, Magnus Eklund, Mark Stambaugh, Martijn O., Martin Harris, Martin Holtham, Martine Nome, Matt Askins, Matt Hutton, Matthew Reynier, Matthew Riggle, Matthew Schulz, Matthew Scroggs, Matthias Planitzer, Maxime Rivet, Maximilian Pfister, Michael DeLyser, Michael Prescott, Mihai Zsisku, Mike Hands, Moritz Stocker, Nadine Chaurand, Nathan Chun, Nick C, Nick Keith, Nick Mohr, Norvin Richards, Olov Wilander, Pamela Docherty, Pau Batlle, Paul Livesey, Pranshu Gaba, Ray Arndorfer, Rea, Reuben Cheung, Riccardo Lani, Richard Pemberton, Rileigh Luczak, Road White, Roni, Rosie Paterson, Russ Collins, Ruth Franklin, Ryan Coomer, Ryan Seldon, Ryan Wise, Sam Dreilinger, Sam Hartburn, Sammie Buzzard, Sara Van Hoy, Sarah Brook, Saul Freedman, Scott, Sean, Sean Carmody, Sean Henderson, Sean McDonald, Sebastian, Selina Glauert, Seth Cohen, Shivanshi Adlakha, Simon Schneider, Sophie Maclean, Spencer B., Stephen Cappella, Stephen Dainty, Stephen Jasina, Steve Blay, Steve Paget, Steven Richardson, Susana Early, Tarim, Tim Holman-Wilkens, Tim Lewis, Todd Geldon, Tom Fryers, Tony Mann, Tristan Shephard, Valentin Valciu, Vinesh, Yasha, Yuliya Nesterova, Yurie Ito, and Zachary Polansky who all also found Santa's house but were too unlucky to win prizes this time.

See you all next December, when the Advent calendar will return.

This year, the front page of mscroggs.co.uk will once again feature an Advent calendar, just like in the five previous Decembers. Behind each door, there will be a puzzle with a three digit solution. The solution to each day's puzzle forms part of a 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.

The residents' clues will reveal to you a seqeunce of compass directions to follow. You can try out your sequences on this map.

Behind each day (except Christmas Day), there is a puzzle with a three-digit answer. Each of these answers forms part of a resident's clue. You must use these clues to work out how to find Santa's house.

Ten randomly selected people who solve all the puzzles, find Santa's house, and fill in the entry form behind the door on the 25th will win prizes!

The winners will be randomly chosen from all those who submit the entry form before the end of 2020. Each day's puzzle (and the entry form on Christmas Day) will be available from 5:00am GMT. But as the winners will be selected randomly, there's no need to get up at 5am on Christmas Day to enter!

As you solve the puzzles, your answers will be stored. To share your stored answers between multiple devices, enter your email address below the calendar and you will be emailed a magic link to visit on your other devices.

To win a prize, you must submit your entry before the end of 2020. Only one entry will be accepted per person. If you have any questions, ask them in the comments below or on Twitter.

So once December is here, get solving! Good luck and have a very merry Christmas!

It's 2020, and the Advent calendar has disappeared, so it's time to reveal the answers and annouce the winners. But first, some good news: with your help, Santa and his two reindeer were found and Christmas was saved!

Now that the competition is over, the questions and all the answers can be found here. Before announcing the winners, I'm going to go through some of my favourite puzzles from the calendar, reveal the solution and a couple of notes and Easter eggs.

My first highlight is this puzzle from 10 December that seems difficult to get started on, but plotting the two quadratics reveals a very useful piece of information that can be used.

My next highlight is the puzzle from 12 December, which was election day in the UK. Although the puzzle isn't that difficult or interesting to calculate, the answer is surprising enough to make this one of my favourites.

My next highlight is the puzzle from 13 December. If you enjoyed this one, then you can find a puzzle based on a similar idea on the puzzles pages of issue 10 of Chalkdust.

My final highlight is the puzzle from 16 December. I always include a few of these, as they can be designed to give any answer so are useful for making the final logic puzzle work. But I was particularly happy with this one.

A few of you may have noticed the relevance of the colours assigned to each island: Rum (Red Rum), Land (Greenland), Moon (Blue Moon), and County (Orange County).

Once you've entered 24 answers, the calendar checks these and tells you how many are correct. I logged the answers that were sent for checking and have looked at these to see which puzzles were the most and least commonly incorrect. The bar chart below shows the total number of incorrect attempts at each question.

You can see that the most difficult puzzles were those on 4 and 15 December; and the easiest puzzles were on 3, 11, 17, and 24 December.

This year, the final logic puzzle revealed the positions of Santa, Rudolph and Blitzen, then you had to find them on this map. The map has 6 levels, with 81 positions on each level, so the total size of the map is \(81^6=282\,429\,536\,481\) squares. This is a lot; one Advent solver even wondered how large a cross stitch of the whole thing would be. I obviously didn't draw 282 billion tiles: the whole map was generated using the following tiles, which were reused across the map.

I also snuck a small Easter egg into the map. Below the Advent calendar, this example was shown:

If you actually visited this position on the map, you found Wally.

At least one Advent solver appears to have found Wally, as they left this cryptic comment under the name Dr Matrix (an excellent Martin Gardner reference).

The solutions to all the individual puzzles can be found here.

Using the daily clues, it was possible to work out that Santa was at 36.11.19.79.79.43, Blitzen was at 23.12.23.11.23.11, and Rudolph was at 16.64.16.16.16.64.

And finally (and maybe most importantly), on to the winners: 126 people found Santa and both reindeer and entered the competition. Their (very) approximate locations are shown on this map:

From the correct answers, the following 10 winners were selected:

Congratulations! Your prizes will be on their way shortly.

The prizes this year include 2019 Advent calendar T-shirts. If you didn't win one, but would like one of these, you can buy one at mscroggs.co.uk/tshirt until 7 January (when I will be sending them for printing).

Additionally, well done to Adam Abrams, Adam NH, Adam Vellender, Alan Buck, Alex Ayres, Alex Burlton, Alexander Ignatenkov, Andrew Ennaco, Andrew Tindall, Artie Smith, Ashley Jarvis, Austin Antoniou, Becky Russell, Ben Jones, Ben Reiniger, Brennan Dolson, Brian Carnes, Carl Westerlund, Carmen Guenther, Clare Wallace, Colin Beveridge, Connie, Corbin Groothuis, Cory Peters, Dan Colestock, Dan DiMillo, Dan Whitman, David, David Ault, David Fox, Diane Keimel, Duncan Ramage, Emilie Heidenreich, Emily Troyer, Eric, Eric Kolbusz, Erik Eklund, Evan Louis Robinson, Frances Haigh, Franklin Ta, Fred Verheul, Félix Breton, Gabriella Pinter, Gautam Webb, Gert-Jan de Vries, Hart Andrin, Heerpal Sahota, Herschel Pecker, Jacob Juillerat, Jan, Jean-Noël Monette, Jen Shackley, Jeremiah Southwick, Jessica Marsh, Johan Asplund, John Warwicker, Jon Foster, Jon Palin, Jonathan Chaffer, Jonathan Winfield, Jose, Kai, Karen Climis, Karen Kendel, Katja Labermeyer, Laura, Lewis Dyer, Louis de Mendonca, M Oostrom, Magnus Eklund, Mahmood Hikmet, Marian Clegg, Mark Stambaugh, Martin Harris, Martine Vijn Nome, Matt Hutton, Matthew Askins, Matthew Schulz, Maximilian Pfister, Melissa Lucas, Mels, Michael DeLyser, Michael Gustin, Michael Horst, Michael Prescott, Mihai Zsisku, Mike, Mikko, Moreno Gennari, Nadine Chaurand, Naomi Bowler, Nathan C, Pat Ashforth, Paul Livesey, Pranshu Gaba, Raymond Arndorfer, Riccardo Lani, Rosie Paterson, Rupinder Matharu, Russ Collins, S A Paget, SShaikh, Sam Butler, Sam Hartburn, Scott, Seth Cohen, Shivanshi Adlakha, Simon Schneider, Stephen Cappella, Stephen Dainty, Steve Blay, Thomas Tu, Tom Anderson, Tony Mann, Yasha, and Yuliya Nesterova, who all also submitted the correct answer but were too unlucky to win prizes this time.

See you all next December, when the Advent calendar will return.