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2016-12-20
Last week, I posted about the Christmas card I designed on the Chalkdust blog.
![](javascript:showlimage("card2016.jpg"))
The card looks boring at first glance, but contains 12 puzzles. Converting the answers to base 3, writing them in the boxes on the front, then colouring the 1s green and 2s red will reveal a Christmassy picture.
If you want to try the card yourself, you can download this pdf. Alternatively, you can find the puzzles below and type the answers in the boxes. The answers will be automatically converted to base 3 and coloured...
| # | Answer (base 10) | Answer (base 3) | ||||||||
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
| 12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
- The square number larger than 1 whose square root is equal to the sum of its digits.
- The smallest square number whose factors add up to a different square number.
- The largest number that cannot be written in the form \(23n+17m\), where \(n\) and \(m\) are positive integers (or 0).
- Write down a three-digit number whose digits are decreasing. Write down the reverse of this number and find the difference. Add this difference to its reverse. What is the result?
- The number of numbers between 0 and 10,000,000 that do not contain the digits 0, 1, 2, 3, 4, 5 or 6.
- The lowest common multiple of 57 and 249.
- The sum of all the odd numbers between 0 and 66.
- One less than four times the 40th triangle number.
- The number of factors of the number \(2^{756}\)×\(3^{12}\).
- In a book with 13,204 pages, what do the page numbers of the middle two pages add up to?
- The number of off-diagonal elements in a 27×27 matrix.
- The largest number, \(k\), such that \(27k/(27+k)\) is an integer.
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2016-12-20
@Matthew: Thank you for the prompt response! It makes sense now and perhaps I should have read a little closer!Dan Whitman
@Dan Whitman: Find the difference between the original number and the reverse of the original. Call this difference \(a\). Next add \(a\) to the reverse of \(a\)... ×1
Matthew
×1 In number 4 what are we to take the difference between? Do you mean the difference between the original number and its reverse? If so when you add the difference back to the reverse you simply get the original number, which is ambiguous. I am not sure what you are asking us to do here.
Dan Whitman
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2016-11-27
This year, the front page of mscroggs.co.uk will feature an advent calendar, just like last year. Behind each door, there will be a puzzle with a three digit solution. The solution to each day's puzzle forms part of a murder mystery logic puzzle in which you have to work out the murderer, motive, location and weapon used: the answer to each of these murder facts is a digit from 1 to 9 (eg. The murderer could be 6, the motive 9, etc.).
As you solve the puzzles, your answers will be stored in a cookie. Behind the door on Christmas Day, there will be a form allowing you to submit your answers. The winner will be randomly chosen from all those who submit the correct answer on Christmas Day. Runners up will then be chosen from those who submit the correct answer on Christmas Day, then those who submit the correct answer on Boxing Day, then the next day, and so on. As the winners will be chosen randomly, there is no need to get up at 5am on Christmas Day this year!
The winner will win this array of prizes:
![](javascript:showlimage("prizes2016.jpg"))
I will be adding to the pile of prizes throughout December. Runners up will get a subset of the prizes. The winner and runners up will also win an mscroggs.co.uk 2016 winners medal:
![](javascript:showlimage("medals2016.jpg"))
To win a prize, you must submit your entry before the end of 2016. Only one entry will be accepted per person. Once ten correct entries have been submitted, I will add a note here and below the calendar. 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!
Edit: added picture of this year's medals.
Edit: more than ten correct entries have been submitted, list of prize winners can be found here.
You can still submit your answers but the only prize left is glory.
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@Another Matthew: Ten correct submissions have been made. Just updating the pages to reflect this...
Matthew
Really enjoyed the extra bit at the end this year! Looking forward to 2017's calendar.
Louis
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2016-01-01
The deadline for entering the 2015 Advent calendar competition has now passed. You can see all the puzzles and their answers here.
Thank-you to everyone who took part in the competition! In total, 23 people submitted answers to the puzzles. Every one of these had correct answers to at least 18 of the puzzles. The winners are as follows:
| # | Name | Details |
| 1 | Scott | All correct at 5:00:18 GMT on Christmas Day |
| 2 | Louis de Mendonca | All correct at 5:00:32 GMT on Christmas Day |
| 3 | Alex Bolton | All correct at 5:00:34 GMT on Christmas Day |
| 4 | Martin Harris | All correct at 6:15 GMT on Christmas Day |
| 5 | Linus Hamilton | All correct at 14:12 GMT on Christmas Day |
| 6 | Zephi | All correct at 20:40 GMT on Christmas Day |
| 7 | Daniel Chiverton | All but one (5 December) correct at 5:00:24 GMT on Christmas Day |
| 8 | Jon Palin | All but one (12 December) correct at 5:00:34 GMT on Christmas Day |
| 9 | Kathryn Coffin | All but one (5 December) correct at 6:28 GMT on Christmas Day |
| 10 | Félix Breton | All but one (15 December) correct at 9:05 GMT on Christmas Day |
I will be in touch will all the entrants in the next few days and I will post pictures of prizes here once they are on their way!
I have already started working on puzzles for next year's (in fact this year's) calendar, so make sure you're back here in December...
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@stephan: It looks like the code I wrote to check the solutions were unique contained errors. This might explain why first question was very difficult to solve with logic alone.
Matthew
Are you sure http://www.mscroggs.co.uk/puzzles/126 have unique solutions. See e.g. http://cryptarithms.awardspace.us/solv... which gives lots of solutions
stephan
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2015-11-24
This year, the front page of mscroggs.co.uk will feature an advent calendar. Behind each door, there will be a puzzle with a three digit solution.
As you solve the puzzles, your answers will be stored in a cookie. Behind the door on Christmas Day, there will be a form allowing you to submit your answers. The first person to submit the correct answers will win this array of prizes:
![](javascript:showlimage("prizes.jpg"))
The prizes include an mscroggs.co.uk t-shirt, a DVD of Full Frontal Nerdity and a beautiful mscroggs.co.uk 2015 winner's medal:
![](javascript:showlimage("medal.jpg"))
I will be adding to the pile of prizes throughout December.
The next nine people to submit the correct answers will win a winner's medal plus a smaller goody bag of prizes. If less than ten correct entries are submitted, prizes will be given to those with one incorrect answer, then those with two incorrect answers and so on.
Each day's puzzle (and the entry form on Christmas Day) will be available from 5:00am GMT.
To win a prize, you must submit your entry before the start of 2016. Only one entry will be accepted per person. Once ten correct entries have been submitted, I will add a note here and below the calendar. 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!
Edit: The winners and answers can now be found here.
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I've submitted my answer! On Christmas too! It's just that I sorta crammed all of the answers today :/
Are you allowed to tell me if I am correct?
Are you allowed to tell me if I am correct?
Anonymous1
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2013-12-23
Here is a collection of Christmas relates mathematical activities.
Flexagons
I first encountered flexagons sometime around October 2012. Soon after, we used this template to make them at school with year 11 classes who had just taken GCSE papers as a fun but mathematical activity. The students loved them. This lead me to adapt the template for Christmas:
![](javascript:showlimage("xmas-flex.png"))
And here is an uncoloured version of the template on that site if you'd like to colour it yourself and a blank one if you'd like to make your own patterns:
![](javascript:showlimage("flex.png"))
![](javascript:showlimage("blank-flex.png")){kind=spacer}
The excitement of flexagons does not end there. There are templates around for six faced flexagons and while writing this piece, I found this page with templates for a great number of flexagons. In addition, there is a fantastic article by Martin Gardner and a two part video by Vi Hart.
Fröbel stars
I discovered the Fröbel star while searching for a picture to be the Wikipedia Maths Portal picture of the month for December 2013. I quickly found these very good instructions for making the star, although it proved very fiddly to make with paper I had cut myself. I bought some 5mm quilling paper which made their construction much easier. With a piece of thread through the middle, Fröbel starts make brilliant tree decorations.
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