Odds and Evenings – Details, episodes & analysis

The boys return to think about the structure of a quiz show round, they learn how to queue effectively and they investigate the best tunings for guitars. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Only Connect Loops Adding a Teller Alternative Tunings Show Notes Queuing Blog (https://www.johndcook.com/blog/2008/10/21/what-happens-when-you-add-a-new-teller/) Cabbage Tuning (https://www.youtube.com/watch?v=cB54IWMWVrc) Under the Bridge Tuning (https://www.youtube.com/watch?v=Daw93bRHe4Y) David's Kingdom Heart Video Series (https://www.youtube.com/watch?v=f11crL1IxSA) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Infeasible App Ideas by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys are in the same room, and they have a guest! They talk about an awful tennis tournament mixup, a teeny tiny card game and the primest day of the year. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Quantum Go Fish Amateur-Professional Tennis Tournament Problem Prime Day Show Notes Some divisbility criteria (https://brilliant.org/wiki/divisibility-rules/) The Trachtenburg System (https://en.wikipedia.org/wiki/Trachtenberg_system) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Guest Matthew - http://mscroggs.co.uk/ Editing by Alex Invisible playing cards supplied by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323 Special Guest: Matthew Scroggs.

The boys get to the bottom of a neat pattern that suddenly breaks, contort their limbs into strange shapes in the name of Plato and attempt a very satisfying problem involving some spiders and an ant. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Factorial Terminating Digits Making Polyhedra with your Limbs Spiders and an Ant Pursuit Puzzle Show Notes Nice PDF of the Solution to the Partitions Problem by André Malraux (https://ufile.io/twukd) Alaric's Puzzle from the Conference (https://twitter.com/OddsAndEvenings/status/1064153315280330752) Platonic Solids to Stare at during Sections 2 and 3 of the Show (https://upload.wikimedia.org/wikipedia/commons/d/d3/Platonic_solids.jpg) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Fervent attempts to keep on top of responding to emails for the show by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys get as spooky as they can with cellular automata, have a maths conversation about maths conversations and can't get past the fact that Brunnian and Borromean sound too similar. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Zombies and Vampires The Maths of Conversations Brunnian Pumpkin Carving Show Notes Follow Up Maths Jam Annual Gathering Page (https://www.solipsys.co.uk/cgi-bin/MJ_Wiki.py?FrontPage) The Shade (Alex's New Podcast) (https://hacking.finance/read/?c=the-shade) Maths From the Show SIR Model Introduction by Alaric (http://www.alaricstephen.com/main-featured/2016/9/24/modelling-a-pandemic) SIR Model You Can Play With (https://docs.google.com/spreadsheets/d/1HxS1GttDPT8eDOhTIfOYckueArSJjGb5VfOr1hgqLno/edit?usp=sharing) Borromean Rings (https://en.wikipedia.org/wiki/Borromean_rings) Brunnian Links (https://en.wikipedia.org/wiki/Brunnian_link)(more generalised) Pochhammer's Countour (https://en.wikipedia.org/wiki/Pochhammer_contour) A Classic Video on Brunnian Links (https://www.youtube.com/watch?v=heKK95DAKms&ab_channel=Vihart) (in the form of snakes), by Vi Hart Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Following of the brief: bring halloween problems by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys settle a dicussion about a bike that Alaric has been aching to talk about for a fortnight, Alex finally brings up music and then they both dive down the Gödel rabbit hole with some puzzles. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Bike Pedals Time Signatures Taking an Offer Puzzles Show Notes Follow Up Visualisation of the Codepad Solution from Tom Verduyn (https://bl.ocks.org/TVerduyn/raw/4935615ba55a2c0b73b2550e0eb8764d/) Maths Jam Annual Gathering Page (https://www.solipsys.co.uk/cgi-bin/MJ_Wiki.py?FrontPage) The Shade (Alex's New Podcast) (https://hacking.finance/read/?c=the-shade) Maths From the Show Visuals of the Two Cycloids Mentioned: Prolate (http://mathworld.wolfram.com/ProlateCycloid.html) and Curtate (http://mathworld.wolfram.com/CurtateCycloid.html) Video of the Bike Moving (https://twitter.com/SingMathsJam/status/1042057017148334080) Unusual Time Signatures (https://en.wikipedia.org/wiki/List_of_musical_works_in_unusual_time_signatures) Forever Undecided: A Puzzle Guide to Gödel (https://www.amazon.co.uk/Forever-Undecided-Puzzle-Guide-Godel/dp/0192801414) The book I talk about in the third part of the show. It's great. The Gödel Sentence on Wikipedia (https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#Truth_of_the_Gödel_sentence) (Related to the puzzle) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Incomplete knowledge of incompleteness theorems by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys design algorithms to generate puzzles on graphs, spiral out into some polar coordinate calculus and gallop their way through some juggling notation. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Untangling Planar Graphs The Length of Spirals Juggling and Horse Gaits Show Notes A Picture of Untangle (http://www.gameclassification.com/files/games/Untangle.png) The Criteria for Planarity (https://en.wikipedia.org/wiki/Kuratowski%27s_theorem) The Two Spirals in Desmos (a graphing calculator) (https://www.desmos.com/calculator/xqqafvcbf9) Arc Length in Polar Form Derivation (http://sites.millersville.edu/bikenaga/calculus/arc-length-in-polar/arc-length-in-polar.html) Jakob Bernoulli's Gravestone (https://www.flickr.com/photos/deaddogbarking/4545328000) Horse Gaits on Wikipedia (https://en.wikipedia.org/wiki/Horse_gait) Negative Juggling Simulator (http://juggle.wikia.com/wiki/Impossible_Siteswap_Animator) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Rather fitting spiral anecdote by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys delve into some stats and game theory problems, ending with a classic from Conway. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Dominion Probabilities The Cheapest Beer in Prague The Angel Problem Show Notes Dominion Probabilities Article (http://www.alaricstephen.com/main-featured/2016/11/28/dominion-probabilities) The Generalised Coupon Collecting Formula in Wolfram Alpha (www.wolframalpha.com) Type this into input: sum from j=0 to 25 of ((-1)^(j)(25 choose j)(((25-j) choose 10)/(25 choose 10))^8) (I couldn't directly link because the % signs in the URL were messing up our site linking. Apologies for the mess. The Secretary Problem (https://en.wikipedia.org/wiki/Secretary_problem) The Angel Problem (by Alaric) (http://www.alaricstephen.com/main-featured/2017/7/12/the-angel-problem) James Grime's Video on the Codepad Problem (https://www.youtube.com/watch?v=iPLQgXUiU14&ab_channel=singingbanana) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Back to school vocals by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys move seemlessly between high philosophy and pirate jokes in this eclectic episode. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Keypad Code Guessing Platonism vs Formalism Pirate Plunder Puzzle Show Notes Pirate Plunder Puzzle (http://www.alaricstephen.com/main-featured/2017/4/10/the-pirate-puzzle) Prisoners in Rainbow Hats (http://www.alaricstephen.com/main-featured/2017/6/13/prisoners-in-rainbow-hats) Z-Order Curves (https://en.wikipedia.org/wiki/Z-order_curve) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Dreams of being a philosopher pirate by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys try their hands at problems provided by the listeners in today's special episode. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed Prisoners in Hats Kaprekar's Constant Generalised Egg Dropping Show Notes Prisoners in Rainbow Hats (http://www.alaricstephen.com/main-featured/2017/6/13/prisoners-in-rainbow-hats) Islander Paradox (http://www.alaricstephen.com/main-featured/2017/4/10/the-islander-paradox) Kaprekar's Constant (https://en.wikipedia.org/wiki/6174_(number)) General Egg Problem Solution (https://stackoverflow.com/questions/11603218/three-egg-problem#) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Too many Hat Problem anecdotes by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323

The boys both have problems which involve complicating the process of adding. Also snakes. Odds and Evenings Twitter - https://twitter.com/OddsAndEvenings Website - http://www.oddsandevenings.com Topics discussed FRACTRAN Negative Bases Polycube Snakes Show Notes FRACTRAN (https://en.wikipedia.org/wiki/FRACTRAN) Adding in Negative Bases (https://en.wikipedia.org/wiki/Negative_base#Addition) Quarter-Imaginary Base (https://en.wikipedia.org/wiki/Quater-imaginary_base) Fascinating Turing Complete Magic the Gathering (https://www.toothycat.net/~hologram/Turing/HowItWorks.html) Article on Polycube Snakes (http://www.alaricstephen.com/main-featured/2017/5/20/polycube-snakes) Credits Hosted By Alaric - http://alaricstephen.com Alex - http://twitter.com/speakmouthwords Editing by Alex Knuth Pronunciation by Alaric Theme music by David Russell - https://youtube.com/DavidRussell323