Prposed Solution to Problem 4
"Solution" by Steve Sayer[Editorial Note: Here is Steve's submitted solution. We will turn thisinto a contest to see if anyone can find a better solution.]
Here's my guess for now: the minimum time is 132 seconds. The pattern is:IITOFIT(B)OFIT(B)OOBwhere I = Put a slice in; O = take a slice out; F = flip a slice in thetoaster; T = toast slices in toaster; B = Butter a toasted orsemi-toasted slice. Brackets mean "meanwhile"; since buttering takes lesstime than toasting, to butter a slice while toasting takes no more timethan toasting alone.Coding each slice as 1, 2, or 3 respectively:1I 2I 12T 1O 2F 3I 23T (1B) 2O 3F 1I 13T (2B) 1O 3O 3B 3+ 3+ 30+ 3+ 3+ 3+ 30+ (0) 3+ 3+ 3+ 30+ (0) 3+ 3+ 12 = 132 seconds.This is most efficient because two slices are always being toasted, and as much buttering is done during toasting as possible.
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