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Christmas (2021) is over
2022-01-08
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.
Highlights
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.
2 December
The number \(7n\) has 37 factors (including 1 and the number itself). How many factors does \(8n\) have?
There was a typo in this puzzle. It originally read "38 factors" when it was meant to say "37 factors".
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.
5 December
How many different isosceles triangles are there whose perimeter is 50 units, and whose area is an integer number of square-units?
(Two triangles that are rotations, reflections and translations of each other are counted as the same triangle. Triangles with an area of 0 should not be counted.)
![](javascript:showlimage("advent2021-isosceles.gif"))
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.
14 December
You start at the point marked A in the picture below. You want to get to the point marked B. You may travel to the right, upwards, or to the left along the black lines, but you cannot pass along the same line segment more than once.
![](javascript:showlimage("advent2021-routes.png"))
Today's number is the total number of possible routes to get from A to B.
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.
16 December
Each clue in this crossnumber is formed of two parts connected by a logical connective:
and means that both parts are true;
nand means that at most one part is true;
or means that at least one part is true;
nor means that neither part is true;
xor means that exactly one part is true;
xnor means that either both parts are false or both parts are true.
No number starts with 0.
|
1A is a palindrome xnor 1D is a palindrome.
1A is greater than 350 nor 1D is less than 150.
3D is odd nand 4A and 2D are equal.
3D is prime xor 5A is odd.
4A is a cube and 2D is a cube.
The sum of the digits of 3D is 2 or the sum of the digits of 5A is 5.
Today's number is 1D.
|
Hardest and easiest puzzles
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.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
| Day | |||||||||||||||||||||||
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.
An Easter egg
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.
![](javascript:showlimage("adcal2021.png"))
This was spotted by
both Colin Beveridge (@icecolbeveridge)
and Alex on 15 December.
The winners
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:
| 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 |
| Year | ||||||
From the correct answers, the following 10 winners were selected:
- Shivanshi
- LycanFayn
- Colin Beveridge
- Katharine Velleman
- Gregory Wheeler
- Alex Bolton
- Don Anderson
- Dan Colestock
- Pamela Docherty
- Annabel
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.
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Comments
Comments in green were written by me. Comments in blue were not written by me.
Damn, missed out again! But had a lot of fun (again). I'd guess the reason for there being fewer successful entries this year was the final puzzle being much harder than previous years, rather than a drop in participation. I got worried I still hadn't solved it on the 30th and had to get my whole family involved!
Louis
Thanks for the advert calendar this year.
By the way, in the "Hardest and easiest puzzles" section, 4 out of the 5 links to the puzzles are to the 2020 puzzles instead of the 2021 puzzles×2 ×2 ×2
By the way, in the "Hardest and easiest puzzles" section, 4 out of the 5 links to the puzzles are to the 2020 puzzles instead of the 2021 puzzles
Alex
×2 ×2 ×2 My son and I really enjoyed solving the puzzles each day. As a mom whose son is thousands of miles away, it was a great way to connect each day of Advent. This is our second year and I will definitely order a tee shirt. Keep up the great work! ×2
Liz
×2 Add a Comment
At least my failed attempt to figure that one made me realize that I needed to change my answer to day 12.