### Riddle 1 Answer

I appear to have left Riddle 1 sitting out there without an official answer for almost seven months now. Sorry about that.

The answer given by Peter Byrne was valid, and essentially the one I was thinking of: while his example dealt with the untyped empty list `()`

, I had the typed empty list ``boolean$()`

in mind.

The insight here is that `any`

and `all`

are forms of `min`

and `max`

; and that `min x,y`

, the min of the concatenation of two lists, is equal to `min(min x;min y)`

, the min of their separate `min`

s (and *mutatis mutandis* for `max`

). For this to work consistently for empty lists, the `min`

of an empty list must be the maximum possible value for that data type (and *mutatis mutandis* for `max`

).

Labels: riddle, riddle answer, theory