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 2020
Christmas card 2019
Christmas card 2018

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
            ×1     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 "e" then "q" then "u" then "a" then "t" then "i" then "o" then "n" in the box below (case sensitive):

Archive

Show me a random blog post
 2021 

Jan 2021

Christmas (2020) is over
 2020 
▼ show ▼
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

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

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2021