mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

Archive

Show me a random blog post
 2019 
 2018 
 2017 
 2016 
 2015 
 2014 
 2013 
 2012 

Tags

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

Archive

Show me a random blog post
▼ show ▼

Christmas card 2017

 2017-12-18 
Just like last year, TD and I spent some time in November this year designing a puzzle Christmas card for Chalkdust.
The card looks boring at first glance, but contains 10 puzzles. Converting the answers to base 3, writing them in the boxes on the front, then colouring the 1s black and 2s orange 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)
10000000
20000000
30000000
40000000
50000000
60000000
70000000
80000000
90000000
100000000
  1. In a book with 116 pages, what do the page numbers of the middle two pages add up to?
  2. What is the largest number that cannot be written in the form \(14n+29m\), where \(n\) and \(m\) are non-negative integers?
  3. How many factors does the number \(2^6\times3^{12}\times5^2\) have?
  4. How many squares (of any size) are there in a \(15\times14\) grid of squares?
  5. You take a number and make a second number by removing the units digit. The sum of these two numbers is 1103. What was your first number?
  6. What is the only three-digit number that is equal to a square number multiplied by the reverse of the same square number? (The reverse cannot start with 0.)
  7. What is the largest three-digit number that is equal to a number multiplied by the reverse of the same number? (The reverse cannot start with 0.)
  8. What is the mean of the answers to questions 6, 7 and 8?
  9. How many numbers are there between 0 and 100,000 that do not contain the digits 0, 1, 2, 3, 4, 5, or 6?
  10. What is the lowest common multiple of 52 and 1066?

Similar posts

Christmas card 2016
Christmas card 2018
Christmas (2018) is over
Christmas (2018) is coming!

Comments

Comments in green were written by me. Comments in blue were not written by me.
 2019-01-04 
@Jose: There is a mistake in your answer: 243 (0100000) is the number of numbers between 10,000 and 100,000 that do not contain the digits 0, 1, 2, 3, 4, 5, or 6.
Reply
Matthew
 2019-01-04 
Thanks for the puzzle!
Is it possible that the question 9 is no correct?
I get a penguin with perfect simetrie except at answer 9 : 0100000 that breaks the simetry.
Is it correct or a mistake in my answer?
Thx
Reply
Jose
 2018-01-01 
@C: look up something called Frobenius numbers. This problem's equivalent to finding the Frobenius number for 14 and 29.
Reply
Lewis
 2017-12-28 
I can solve #2 with code, but is there a tidy maths way to solve it directly?
Reply
C
 2017-12-23 
My efforts were flightless.
Reply
NHH
 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 "tneitouq" backwards in the box below (case sensitive):
© Matthew Scroggs 2019