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-first day of the 2016 Chalkdust Advent Calendar. Today, we bring you our final selection of fascinatingT&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.

This post was part of the Chalkdust 2016 Advent Calendar.

Find your perfect partner with this wonderful tree diagram!

[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.

Behind today’s door… A quiz!

[playbuzz-item url=”//www.playbuzz.com/rafael12/maths-trivia”]

[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]

# The Chalkdust Christmas card

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.

### Christmas Card 2016

The grid (click to enlarge)

#### Instructions

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

#### Puzzles

1. The square number larger than 1 whose square root is equal to the sum of its digits.
2. The smallest square number whose factors add up to a different square number.
3. The largest number that cannot be written in the form $23n+17m$, where $n$ and $m$ are positive integers (or 0).
4. 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?
5. The number of numbers between 0 and 10,000,000 that do not contain the digits 0, 1, 2, 3, 4, 5 or 6.
6. The lowest common multiple of 57 and 249.
7. The sum of all the odd numbers between 0 and 66.
8. One less than four times the 40th triangle number.
9. The number of factors of the number 2756×312.
10. In a book with 13,204 pages, what do the page numbers of the middle two pages add up to?
11. The number of off-diagonal elements in a 27×27 matrix.
12. The largest number, $k$, such that $27k/(27+k)$ is an integer.