*This post was part of the Chalkdust 2016 Advent Calendar.*

Today is the final day of the Chalkdust advent calendar.

A magazine for the mathematically curious

Advent calendar

*This post was part of the Chalkdust 2016 Advent Calendar.*

Today is the final day of the Chalkdust advent calendar.

*This post was part of the Chalkdust 2016 Advent Calendar.*

Welcome to the twenty third day of the 2016 Chalkdust Advent Calendar. Today, we have another puzzle for you to enjoy, plus the answer to the puzzles from 12 December.

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*This post was part of the Chalkdust 2016 Advent Calendar.*

Welcome to the 22nd day of the 2016 Chalkdust Advent Calendar. Today we have for you, a book review!

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*This post was part of the Chalkdust 2016 Advent Calendar.*

Welcome to the twenty-first day of the 2016 Chalkdust Advent Calendar. Today, we bring you our final selection of fascinating^{T&Cs apply} facts, randomly generated by Santa’s elves. Remember to send us your favourite scientific curiosities via Facebook, Twitter or email and we’ll feature the best in a blog next year.

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*This post was part of the Chalkdust 2016 Advent Calendar.*

Welcome to the 20th day of the 2016 Chalkdust Advent Calendar. Today we have yet another Christmaths Carol!

*This post was part of the Chalkdust 2016 Advent Calendar.*

Find your perfect partner with this wonderful tree diagram!

Attributions:

[Cauchy – By Public domain – Library of Congress Prints and Photographs Division. From an illustration in: Das neunzehnte Jahrhundert in Bildnissen / Karl Werckmeister, ed. Berlin : Kunstverlag der photographische gesellschaft, 1901, vol. V, no. 581., Public Domain ; Knot – adapted from Flickr.com – knotted by Shelby Steward, CC-BY 2.0; Emmy Noether – By Unknown – Emmy Noether (1882-1935), Public Domain ; Python – adapted from Flickr.com – Python by Jonathan Kriz, CC-BY 2.0; Daniel Bernoulli – By Johann Jakob Haid – Here, Public Domain ; Scrooge – adapted from Flickr.com – Money by Tax Credits, CC-BY 2.0]

*This post was part of the Chalkdust 2016 Advent Calendar.*

*This post was part of the Chalkdust 2016 Advent Calendar.*

Behind today’s door… A quiz!

Attributions:

[Pictures: 1 – adapted from Flickr.com – Pi by Tom Magliery, CC-BY 2.0; 2 – adapted from Flickr.com – IMG_8118 by SAITOR, CC-BY 2.0; 3 – adapted from Flickr.com – Chichen Itza Pyramid by Shayne Bowman, CC-BY 2.0; 4 – adapted from Flickr.com – Chichen Itza Pyramid by Shayne Bowman, CC-BY 2.0; 5 – adapted from Flickr.com – Pac Man Board Game by Ian Crowfeather, CC-BY 2.0; 6 – adapted from Flickr.com – Keys grid with guide grid by Greg Borenstein, CC-BY 2.0; 7 – adapted from Flickr.com – Ellipses by Eric Wagner, CC-BY 2.0; 8 – adapted from Flickr.com – Equals by Mrs TeePot CC-BY 2.0; 9 – adapted from Flickr.com – Equals by Mrs TeePot CC-BY 2.0; other pictures by Chalkdust]

*This post was part of the Chalkdust 2016 Advent Calendar.*

Recently, some of you may have received a Chalkdust Christmas card. If not, it’s not because we hate you, it’s just that we couldn’t find your address… Unless we hate you, in which case it *is* because we hate you.

The card initially looks very boring: it is just a grid of squares with “Merry Christmas” written below it. Definitely NOT HOT… But there’s more. There’s a puzzle inside that leads you to add some colour to the squares to reveal a Christmassy picture.

Without giving any more away, here is the puzzle. If you’d like to give it to someone as a Christmas card (or just want to actually be able to colour it in), you can print and fold this lovely pdf.

- Solve the puzzles below.
- Convert the answers to base 3.
- Write the answers in the boxes on the front cover.
- Colour squares containing a 1 green. Colour squares containing a 2 red. Leave squares containing a 0 unshaded.

- 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.