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In this episode of Wrong, But Useful:

- @reflectivemaths and I are joined by special guest co-host Elizabeth A. Williams, who is @realityminus3 in real life (and Zeke, who is Zeke everywhere)
- Dave picks 367 as number of the episode, as it's the largest number whose square has digits in strictly increasing order (134,689). Colin notes that the first ten digits of the cube root of 2017 are all distinct.
- Elizabeth brings up @RobJLow's MathsJam talk about balanced ternary
- Shoutouts to:
- @christianp on his Mersenne prime birthday - many happy returns
- @mathjem for writing resourceaholic.com and running...

- ... the Maths World Cup.
- "Pythagoras is about squares."
- Colin goes in for maths comedy.
- Dave protests about the poor showing of stats in the World Cup, blaming the draw, the referees, and just about everything except stats being rubbish.

- Dave is reading Maths Fables by Greg Tang and Heather Cahoon. We also mention Alex Bellos's books (... in Numberland and ... through the Looking Glass) and Colin's Cracking Mathematics.
- Carnival news: @peterrowlett is hosting the next MTaP, and @shahlock is hosting the next Carnival of Mathematics
- @peterrowlett is annoyed about jealous husbands and has tried to put them right. Colin had similar problems trying to translate
*Récréations Mathematiques*. Dave looks into 'best buy questions'. - Colin stumbled across the Sieve of Sundaram and thought it was cool.
- Dave looks at oblong spheres, and explains to Colin that it's either a strict rectangle, or a shape that's longer than wide.
- Gold star to @chrishazell72 for finding the 364 gifts from last time, going up to 2,600 over a 24-day Christmas. Gifts 6 and 7 are the most common in the original song, with 42 of each.
- Elizabeth suggests a reason for $\nCr{14}{3}$ being the number of gifts over 12 days, but Colin is ungraciously unsatisfied.
- Dave's turn for a puzzle or two.
- (1) The exterior angles of a closed polygon sum to 360º (2π radians) - but where, exactly, is the exterior angle at a concave vertex?
- (2) There are two closed boxes in front of you. Box A contains £1,000, and Box B contains either nothing or £1,000,000. You may take either both boxes, or just Box B. A super-intelligent being, with a 100% success rate in predicting such things, has made a prediction about what you'll do; if she predicted you would take both boxes, she left Box B empty; otherwise, it contains the cheque. Assuming you want to make as much money as possible, what should you do?

* If you'd like to be a guest co-host, get in touch with Colin via twitter.