mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

Christmas (2022) is over

 2023-01-08 
Welcome to 2023 everyone! Now that the Advent calendar has disappeared, it's time to reveal the answers and announce the winners. But first, some good news: with your help, the drones were all destroyed in time for Santa to deliver presents 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 and a couple of other interesting bits and pieces.

Highlights

My first highlight is the puzzle from 1 December. I like this puzzle, because the lines of symmetry of a rectangle that you might expect—although it's not too hard to see what the lines of symmetry are, so this makes a nice gentle first puzzle.

1 December

One of the vertices of a rectangle is at the point \((9, 0)\). The \(x\)-axis and \(y\)-axis are both lines of symmetry of the rectangle.
What is the area of the rectangle?

Show answer


My next hightlight is the puzzle from 11 December. I always enjoy a surprise appearance of the Fibonacci sequence.

11 December

There are five 3-digit numbers whose digits are all either 1 or 2 and who do not contain two 2s in a row: 111, 112, 121, 211, and 212.
How many 14-digit numbers are there whose digits are all either 1 or 2 and who do not contain two 2s in a row?

Show answer


My next highlight is the puzzle from 13 December. I love a good crossnumber, and had a lot of fun making this small one up. (If you enjoyed this one, you should check out the crossnumbers I write for Chalkdust.)

13 December

Today's number is given in this crossnumber. The across clues are given as normal, but the down clues are given in a random order: you must work out which clue goes with each down entry and solve the crossnumber to find today's number. No number in the completed grid starts with 0.

Show answer


My final highlight is the puzzle from 24 December. You could solve this by doing a lot of expanding, but there's a neat shortcut that makes it almost trivial to solve.

24 December

The expression \((3x-1)^2\) can be expanded to give \(9x^2-6x+1\). The sum of the coefficients in this expansion is \(9-6+1=4\).
What is the sum of the coefficients in the expansion of \((3x-1)^7\)?

Show answer

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.
You can see that the most difficult puzzles were those on 11, 18 and 19 December; and the easiest puzzle was on 8 December.

The winners

And finally (and maybe most importantly), on to the winners: 192 people managed to destroy all three drones. That's more people than last year:
From the correct answers, the following 10 winners were selected:
Congratulations! Your prizes will be on their way shortly.
The prizes this year include 2022 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 Johnson, Aaron Stiff, Aidan Dodgson, Alejandro Villarreal, Alek2ander, Alex Bolton, Alex Davis, Alex Hartz, Andrew Brady, Andrew Brodie, Andrew Ennaco, Andrew Roy, Andrew Turner, Artie Smith, Ashton Lewis, Austin Antoniou, Becky Russell, Ben Baker, Ben Boxall, Ben Reiniger, Ben Tozer, Ben Weiss, Beth Jensen, Blake, Brennan Dolson, Brian Carnes, Brian Wellington, Carl Westerlund, Carmen, Charleston W, Chris Eagle, Chris Hellings, Colin Beveridge, Colin Brockley, Connie, Corbin Groothuis, CreativeCrocheter, Dan Colestock, Dan DiMillo, Dan May, Dan Swenson, Dan Whitman, Daniel Cuneo, David and Ivy Walbert, David Ault, David Berardo, David Fox, David Kendel, David Mitchell, Deborah Tayler, Deborah Tayler, Derek Perrin, Dominik Niemand, Don Anderson, Dr Lizzie, Duncan Schaafsma, Dylan Richard, Eleanor, Elizabeth Blackwell, Elizabeth Madisetti, Emilie Heidenreich, Emily Troyer, Emma, Eoin Davey, Eric Kolbusz, Eric Scotti, Erik Eklund, Fionn Woodcock, Frances, Frank Kasell, Fred Verheul, Freddie Mao, Félix Breton, Gabriella Pinter, Gary M. Gerken, Gerry, Gert-Jan, Greg W., Gregory Loges, Greta, Han Whiteoak, Hannah Charman, Heerpal Sahota, Helen F, Herschel, Iris, Jack, Jacob, Jacob Loader, James Chapman, James Cunnane, Jarvis9, Jean-Noël Monette, Jean-Sébastien Turcotte, Jen Sparks, Jessica Marsh, Jim Ashworth, Jon Palin, Jonathan Chaffer, Jonathan Thiele, Jorge del Castillo Tierz, Joseph Gage, Joseph Wagner, Joshua Park, Karen Climis, Kevin Docherty, Kirsty Fish, Kristen Koenigs, Kyle Allen, Lazar Ilic, Lewis Dyer, Lise Andreasen, Louis, LycanFayn, Lyra, Magnus Eklund, Marco van der Park, Mark Stambaugh, Martin Harris, Martin Holtham, Mathryn, Matt Thomson, Mels, Merrilyn, Michael DeLyser, Mihai Zsisku, Mike L, Mike R, Millie, Mr J Winfield, Nadine Chaurand, Nancy Walker, Naomi Bowler, Naomi C, Nick Keith, Niji Ranger, Pamela Docherty, Patrick, Philip Corradi, Priyesh, Pup, Qaysed, Qaysed, Rashi, Ray Arndorfer, Reid, Reuben, Riccardo Lani, Rob Dixon, Robert Brady, Roger Lipsett, Roni Malek, Rosie Paterson, Russ Collins, Ruth Franklin, Sage Robinson, Sam Drei, Sarah Brook, Scott, Sean Henderson, Seth Cohen, shadorfff, Simon English, Stephen Cappella, Stephen Jasina, Sumaya Felic, Tamara Brenner, Tarim, The Connors of York, The Steelblade, Tom Fryers, Tony Mann, tripleboleo, Tyler St Clare, UsrBinPRL, Valentin VĂLCIU, Vinayak, Vinny R, vortex, Yasha, Yuliya N., and Zoran Morrissey-Ralevic. 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.
Edit: Removed myself (and a second copy of myself) from the list of solvers.
×3      ×3      ×3      ×3      ×3
(Click on one of these icons to react to this blog post)

You might also enjoy...

Comments

Comments in green were written by me. Comments in blue were not written by me.
You didn't mention the rate limiting you put in for the bots!

Sorry about that
(anonymous)
×6   ×6   ×9   ×7   ×7     Reply
I fought very hard to solve the middle "here are the 6 answers, construct the 6 small problems", but I just couldn't. Hints about that one and the genre in general would be great.
Lise Andreasen
×7   ×7   ×7   ×7   ×7     Reply
@Valentin V?LCIU: Oops, forgot to remove my testing that everything works from the list of people! (Removing it now)
Matthew
×5   ×6   ×6   ×6   ×3     Reply
You solved your own problems? Twice?
Valentin V?LCIU
×3   ×3   ×4   ×3   ×4     Reply
@(anonymous): There was a typo - I've just corrected it
Matthew
×3   ×3   ×3   ×3   ×3     Reply
 Add a Comment 


I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li> <logo>
To prove you are not a spam bot, please type "l" then "i" then "n" then "e" then "a" then "r" in the box below (case sensitive):

Archive

Show me a random blog post
 2024 

Feb 2024

Zines, pt. 2

Jan 2024

Christmas (2023) is over
 2023 
▼ show ▼
 2022 
▼ show ▼
 2021 
▼ show ▼
 2020 
▼ show ▼
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

matt parker quadrilaterals pizza cutting puzzles manchester dinosaurs anscombe's quartet logic recursion manchester science festival matrix of cofactors simultaneous equations platonic solids ternary python squares boundary element methods christmas trigonometry mathsteroids game show probability reddit speed craft propositional calculus london underground radio 4 martin gardner bubble bobble preconditioning javascript london christmas card mathslogicbot braiding pi approximation day geometry 24 hour maths mathsjam zines gaussian elimination determinants matrix of minors fonts golden spiral crochet numbers curvature tennis big internet math-off latex misleading statistics numerical analysis royal baby map projections dataset youtube fence posts go coins people maths edinburgh final fantasy estimation realhats geogebra draughts royal institution weak imposition talking maths in public sport folding tube maps folding paper world cup triangles advent calendar approximation menace databet probability hexapawn finite group european cup tmip a gamut of games data gather town noughts and crosses golden ratio pi chalkdust magazine data visualisation oeis stirling numbers computational complexity gerry anderson pascal's triangle football newcastle php live stream rhombicuboctahedron dragon curves reuleaux polygons books accuracy nine men's morris inverse matrices rugby hannah fry stickers captain scarlet video games statistics games sorting dates ucl interpolation logo guest posts standard deviation turtles harriss spiral cambridge chess graphs weather station pac-man runge's phenomenon frobel bempp raspberry pi hyperbolic surfaces machine learning electromagnetic field phd flexagons wool polynomials finite element method convergence hats binary inline code programming arithmetic crossnumber mean national lottery chebyshev asteroids cross stitch errors fractals light palindromes exponential growth plastic ratio matrix multiplication sound countdown error bars graph theory logs correlation pythagoras wave scattering datasaurus dozen bodmas news the aperiodical sobolev spaces signorini conditions matrices game of life

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2024