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 2018
TMiP 2019 treasure punt
Christmas (2018) is over

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 "uncountable" in the box below (case sensitive):

Archive

Show me a random blog post
 2019 

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

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

Archive

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