One day in 1991(?) I was using a bulky formula in Abramowitz and Stegun "Handbook of Mathematical Function". For parameter values I was interested in, to my surprise, the formula instructed me to raise i to the power of some complex number. I was amazed I could do it and still get a reasonable answer!
Raising i to i seemed like the pure fun, and I asked some of my friends at Lick Observatory to do it infinitely many times. (That is, I didn't ask infinitely many times...) Some declined, thinking it'll take too much (infinite?) time but Willy Kley, then a postdoc in Santa Cruz, went to the trouble of finding the answer.
In 1995 I posed the full two-part problem in the coffee room of the Stockholm Observatory in Saltsjöbaden and offered 2 bottles of good (imported) beer for part one, and 2 bottles of good wine for part two.
Actually, initially it was to be 1 bottle of each (since the problem is NOT THAT difficult!), but that small number 1 plus a less visible place where I advertised the problem resulted in nobody claiming the prize for some time.
Whichever correction was more important, it worked. After a short time first Felix Ryde (a graduate student) solved the first part of the puzzle reproducing Kley's result. Hans Olofsson (professor) made a good progress toward the solution using his calculator too. Later Juri Poutanen (then a postdoc) first solved the second part of the puzzle. The results were published on the coffee room wall and the winners were rewarded with the liquids at one of the traditional ceremonies of Onsdags Bullar (Wednesaday Cakes) at 3pm.
The coffee room is to the right of this entrance.
The tradition of astro-math puzzles soon declined. Everybody seemed too busy doing astronomy to invent new puzzles. (Solving the ones from the books was considered less fun.)
This unfortunate situation continues until today... but at least we have always strictly followed the custom of Onsdags Bullar.