mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

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 2019
Christmas card 2018
Christmas (2019) is over

Comments

Comments in green were written by me. Comments in blue were not written by me.
@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.
Matthew
                 Reply
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
Jose
                 Reply
@C: look up something called Frobenius numbers. This problem's equivalent to finding the Frobenius number for 14 and 29.
Lewis
                 Reply
I can solve #2 with code, but is there a tidy maths way to solve it directly?
C
                 Reply
My efforts were flightless.
NHH
                 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 "etik" backwards in the box below (case sensitive):

Archive

Show me a random blog post
 2020 

Jul 2020

Happy τ+e-6 Approximation Day!

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

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

Archive

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