mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

 2023-09-02 
This week, I've been at Talking Maths in Public (TMiP) in Newcastle. TMiP is a conference for anyone involved in—or interested in getting involved in—any sort of maths outreach, enrichment, or public engagement activity. It was really good, and I highly recommend coming to TMiP 2025.
The Saturday morning at TMiP was filled with a choice of activities, including a puzzle hunt written by me: the Tyne trial. At the start/end point of the Tyne trial, there was a locked box with a combination lock. In order to work out the combination for the lock, you needed to find some clues hidden around Newcastle and solve a few puzzles.
Every team taking part was given a copy of these instructions. Some people attended TMiP virtually, so I also made a version of the Tyne trial that included links to Google Street View and photos from which the necessary information could be obtained. You can have a go at this at mscroggs.co.uk/tyne-trial/remote. For anyone who wants to try the puzzles without searching through virtual Newcastle, the numbers that you needed to find are:
The solutions to the puzzles and the final puzzle are below. If you want to try the puzzles for yourself, do that now before reading on.

Puzzle for clue #2: Palindromes

We are going to start with a number then repeat the following process: if the number you have is a palindrome, stop; otherwise add the number to itself backwards. For example, if we start with 219, then we do: $$219\xrightarrow{+912}1131\xrightarrow{+1311}2442.$$ If you start with the number \(10b+9\) (ie 59), what palindrome do you get?
(If you start with 196, it is unknown whether you will ever get a palindrome.)

Show solution

Puzzle for clue #3: Mostly ones

There are 12 three-digit numbers whose digits are 1, 2, 3, 4, or 5 with exactly two digits that are ones. How many \(c\)-digit (ie 1838-digit) numbers are there whose digits are 1, 2, 3, 4, or 5 with exactly \(c-1\) digits (ie 1837) that are ones?

Show solution

Puzzle for clue #4: is it an integer?

The largest value of \(n\) such that \((n!-2)/(n-2)\) is an integer is 4. What is the largest value of \(n\) such that \((n!-d)/(n-d)\) (ie \((n!-1931)/(n-1931)\)) is an integer?

Show solution

Puzzle for clue #5: How many steps?

We are going to start with a number then repeat the following process: if we've reached 0, stop; otherwise subtract the smallest prime factor of the current number. For example, if we start with 9, then we do: $$9\xrightarrow{-3}6\xrightarrow{-2}4\xrightarrow{-2}2\xrightarrow{-2}0.$$ It took 4 steps to get to 0. What is the smallest starting number such that this process will take \(e\) (ie 1619) steps?

Show solution

Puzzle for clue #6: Four-digit number

I thought of a four digit number. I removed a digit to make a three digit number, then added my two numbers together. The result is \(200f+127\) (ie 9727). What was my original number?

Show solution

Puzzle for clue #7: Dice

If you roll two six-sided fair dice, the most likely total is 7. What is the most likely total if you rolled \(1470+g\) (ie 2470) dice?

Show solution

The final puzzle

The final puzzle involves using the answers to the five puzzles to find the four digit code that opens the box (and the physical locked box that was in the library on Saturday. To give hints to this code, each clue was given a "score".
The score of a number is the number of values of \(i\) such that the \(i\)th digit of the code is a factor of the \(i\)th digit of the number. For example, if the code was 1234, then the score of the number 3654 would be 3 (because 1 is a factor of 3; 2 is a factor of 6; and 4 is a factor of 4).
The seven clues to the final code are:

Show solution

×5      ×4      ×4      ×4      ×4
(Click on one of these icons to react to this blog post)

You might also enjoy...

Comments

Comments in green were written by me. Comments in blue were not written by me.
 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> <logo>
To prove you are not a spam bot, please type "oitar" backwards in the box below (case sensitive):

Archive

Show me a random blog post
 2024 

Feb 2024

Zines, pt. 2

Jan 2024

Christmas (2023) is over
 2023 
▼ show ▼
 2022 
▼ show ▼
 2021 
▼ show ▼
 2020 
▼ show ▼
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

raspberry pi fractals weak imposition palindromes map projections finite group game of life accuracy final fantasy game show probability preconditioning realhats chess fonts logic geometry errors chebyshev light hexapawn python statistics standard deviation coins inverse matrices inline code mathsjam youtube speed probability correlation estimation puzzles electromagnetic field turtles royal baby fence posts trigonometry manchester sorting football guest posts gaussian elimination flexagons tennis graph theory pizza cutting runge's phenomenon reddit mathsteroids christmas card ucl video games rhombicuboctahedron hats graphs logs gerry anderson dragon curves draughts pac-man asteroids computational complexity a gamut of games programming boundary element methods folding tube maps dinosaurs edinburgh geogebra london craft christmas sport manchester science festival pi error bars royal institution frobel cambridge countdown golden ratio stickers phd books propositional calculus pascal's triangle numbers interpolation london underground finite element method weather station mathslogicbot misleading statistics cross stitch wave scattering live stream advent calendar gather town polynomials bubble bobble numerical analysis quadrilaterals pythagoras games bempp mean latex squares world cup plastic ratio anscombe's quartet martin gardner crochet news noughts and crosses the aperiodical simultaneous equations matrix of minors rugby approximation databet ternary talking maths in public big internet math-off determinants javascript matrix multiplication oeis platonic solids php dataset newcastle pi approximation day datasaurus dozen 24 hour maths curvature triangles binary go sound chalkdust magazine signorini conditions matt parker logo golden spiral people maths radio 4 dates sobolev spaces nine men's morris recursion stirling numbers national lottery matrices hannah fry tmip matrix of cofactors folding paper menace captain scarlet machine learning arithmetic exponential growth data visualisation bodmas zines crossnumber hyperbolic surfaces convergence european cup wool data harriss spiral braiding reuleaux polygons

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2024