In this episode, we're joined by special guest co-host @sophiebays, who is Dr Sophie Carr in real life, and the world's most interesting mathematician1.

We discuss:

• The Big Internet Math-Off. My favourite pitch wasn’t really in the contest!
  I also liked Alex’s wobbly table and Anna’s FURNACE.
• Number of the podcast: 24.
• The Winton Centre Quick Quiz for Legal Professionals from @dspiegel.
• Maths Scholarships
• The £50 note.
• The Maryam Mirzakhani Prize in Mathematics.
• The Isaac Newton Institute’s summer puzzles
• Eliasson exhibition at Tate Modern
• What has 4 letters, sometimes 9 letters, but never has 5 letters.
• A claim by Claire’s Accessories.
• Catriona Shearer’s book is available on Amazon: Geometry Puzzles in Felt Pen.
• Puzzle feedback from last time: The average distance of two points in a unit square. No solutions received! (It’s 0.5214 ish, the result of a tricky double integral.)
• New Puzzle via @ghast_neoh: There are two players, and a machine that outputs a random number between 0.0 and 1.0 when you press a button (inclusive, chosen uniformly and independently, from the reals, etc). Player 1 pushes the button twice, and multiplies the two outputs together to get a score (e.g. 0.45 x 0.9=0.4). Then player 2 pushes the button once, and squares the result to get their score (e.g. 0.67 x 0.67 = 0.4489). The higher score wins. Which player wins more often?

1. apparently there are caveats.

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