mscroggs.co.uk
mscroggs.co.uk

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 over

Comments

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

Archive

Show me a random blog post
 2020 

May 2020

A surprising fact about quadrilaterals
Interesting tautologies

Mar 2020

Log-scaled axes

Feb 2020

PhD thesis, chapter ∞
PhD thesis, chapter 5
PhD thesis, chapter 4
PhD thesis, chapter 3
Inverting a matrix
PhD thesis, chapter 2

Jan 2020

PhD thesis, chapter 1
Gaussian elimination
Matrix multiplication
Christmas (2019) is over
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

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

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2020