mscroggs.co.uk
mscroggs.co.uk
Click here to win prizes by solving the mscroggs.co.uk puzzle Advent calendar.
Click here to win prizes by solving the mscroggs.co.uk puzzle Advent calendar.

subscribe

Blog

Christmas card 2016

 2016-12-20 
Last week, I posted about the Christmas card I designed on the Chalkdust blog.
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)
1000000000
2000000000
3000000000
4000000000
5000000000
6000000000
7000000000
8000000000
9000000000
10000000000
11000000000
12000000000
  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 \(2^{756}\)×\(3^{12}\).
  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.

Similar posts

Christmas card 2017
Christmas card 2019
Christmas card 2018
Christmas (2019) is coming!

Comments

Comments in green were written by me. Comments in blue were not written by me.
 2016-12-20 
@Matthew: Thank you for the prompt response! It makes sense now and perhaps I should have read a little closer!
Reply
Dan Whitman
 2016-12-20 
@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 \(a\)...
Reply
Matthew
 2016-12-20 
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.
Reply
Dan Whitman
 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>
To prove you are not a spam bot, please type "ratio" in the box below (case sensitive):

Archive

Show me a random blog post
 2019 

Dec 2019

Christmas card 2019

Nov 2019

Christmas (2019) is coming!

Sep 2019

A non-converging LaTeX document
TMiP 2019 treasure punt

Jul 2019

Big Internet Math-Off stickers 2019

Jun 2019

Proving a conjecture

Apr 2019

Harriss and other spirals

Mar 2019

realhats

Jan 2019

Christmas (2018) is over
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

dates reddit manchester science festival folding tube maps python chalkdust magazine final fantasy polynomials realhats javascript hexapawn captain scarlet advent calendar game show probability inline code error bars mathslogicbot light news programming mathsjam accuracy cross stitch binary european cup weather station tmip wool countdown latex electromagnetic field pythagoras twitter stickers frobel speed sport fractals map projections bubble bobble games oeis pizza cutting raspberry pi coins london sound cambridge curvature puzzles triangles chebyshev flexagons matt parker dragon curves the aperiodical people maths trigonometry golden spiral bodmas football big internet math-off asteroids platonic solids sorting hats plastic ratio talking maths in public statistics game of life machine learning world cup interpolation tennis video games draughts graph theory ternary mathsteroids national lottery books geometry chess arithmetic go folding paper propositional calculus dataset christmas misleading statistics manchester approximation royal baby nine men's morris php noughts and crosses braiding probability radio 4 rhombicuboctahedron golden ratio harriss spiral gerry anderson martin gardner a gamut of games estimation london underground data menace craft logic christmas card palindromes pac-man rugby reuleaux polygons

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2019