The UK game show "The Crystal Maze" features a puzzle based around a totem pole.
The contestant has four different coloured blocks which can be stacked up to make a totem pole. The blocks may be stacked in any order, but there is a single "correct" configuration, which is unknown to the contestant.
Once all four blocks are stacked, the contestant is told how many blocks are currently correctly positioned (but not WHICH blocks). The contestant is obliged to stack all four blocks before being told how many are correct.
The contestant can try as many times as they like, but they are working within a time limit.
Keep in mind, the blocks are heavy and awkward, so there is a time advantage to a strategy that minimises the amount of stacking and re-stacking of the tower. For example, it's faster to swap the top two blocks than it is to exchange the top and bottom blocks.
What's the optimal strategy for the contestant to solve this puzzle as fast as possible?
EDIT - For the sake of argument, let us say that it takes 1 second to remove a block from the top of the stack (however high the stack currently is), and 1 second to put a block on top of the stack.
So, building the complete stack from scratch takes 4 seconds. Swapping the top 2 blocks takes 4 seconds too:
1s to remove top block 1s to remove second block 1s to put the old top block back on in second place 1s to put the former second block on the top
Swapping the top and the bottom blocks would take 8 seconds:
4s to completely disassemble the stack 4s to rebuild the whole thing
There is only one special spot where you can build the stack - you can't optimise by taking the top block off and putting it down somewhere else to start a new stack.