Ladies’ Night

Is a legal chess game possible in which all the pawns promote and each player has nine queens?

Yes — Freidrich Burchard of Germany and Friedrich Hariuc of Romania reached nearly identical solutions in 1980:

1. e4 f5 2. e5 Nf6 3. exf6 e5 4. g4 e4 5. Ne2 e3 6. Ng3 e2 7. h4 f4 8. h5 fxg3 9. h6 g5 10. Rh4 gxh4 11. g5 g2 12. g6 Bg7 13. hxg7 g1=Q 14. f4 h3 15. f5 h2 16. b4 a5 17. b5 a4 18. b6 a3 19. Bb2 Ra7 20. bxa7 axb2 21. a4 b5 22. a5 b4 23. a6 b3 24. c4 h1=Q 25. c5 h5 26. c6 Bb7 27. cxb7 c5 28. d4 c4 29. d5 Nc6 30. dxc6 c3 31. c7 c2 32. c8=Q c1=Q 33. b8=Q Qc7 34. a8=Q d5 35. a7 d4 36. Nc3 dxc3 37. Qa6 c2 38. Qa8b7 c1=Q 39. a8=Q Qd5 40. gxh8=Q+ Kd7 41. g7 bxa1=Q 42. g8=Q b2 43. f7 b1=Q 44. f8=Q h4 45. f6 h3 46. f7 h2 47. Qfa3 h1=Q 48. f8=Q exf1=Q+

18 queens

This may be the shortest possible such game.

Actual Size

The familiar Mercator projection is useful for navigation, but it exaggerates the size of regions at high latitudes. Greenland, for example, appears to be the same size as South America, when in fact it’s only one eighth as large.

An equal-area projection such as the Mollweide, below, distorts the shapes of regions but preserves their relative size. This reveals some surprising facts: Russia is larger than Antarctica, Mexico is larger than Alaska, and Africa is just mind-bogglingly huge — larger than the former Soviet Union, larger than China, India, Australia, and the United States put together.


  • The telephone number 266-8687 spells both AMOUNTS and CONTOUR.
  • 38856 = (38 – 85) × 6
  • CARTHORSE is an anagram of ORCHESTRA.
  • The French for paper clip is trombone.
  • “The oldest books are only just out to those who have not read them.” — Samuel Butler

Gilbreath’s Conjecture

Doodling on a napkin in 1958, mathematician Norman L. Gilbreath noticed something odd. First he wrote down the first few prime numbers in a row. Then, on each succeeding row, he recorded the (unsigned) difference between each pair of numbers in the row above:

gilbreath's conjecture

The first digit in each row (except the first) is 1. Will this always be true, no matter how many prime numbers we start with? It’s been borne out in computer searches extending to hundreds of billions of rows. But no one knows for sure.

Person to Person

Suppose that you enter a cubicle in which, when you press a button, a scanner records the states of all the cells in your brain and body, destroying both while doing so. This information is then transmitted at the speed of light to some other planet, where a replicator produces a perfect organic copy of you. Since the brain of your Replica is exactly like yours, it will seem to remember living your life up to the moment when you pressed the button, its character will be just like yours, and it will be in every other way psychologically continuous with you. Is it you?

— Derek Parfit, “Divided Minds and the Nature of Persons,” in Mindwaves, 1987