When W.G. invited us to his party he rewired the buttons' panel in the elevator and placed next to it a note:
The fun starts here and now. Originally the numbers were in sequence in a way that numbers 1 and 2 were neighbors - horizontally or vertically, 2 and 3 likewise and so on.
Now on 8 of 16 buttons the numbers were erased and then on 4 additional buttons the original numbers were replaced by the wrong ones.
Restore the original layout, press button 15 and join the fun!
Pressing any other button will get you 90 seconds or less of elevator music and a free ride to a wrong floor...
Can you locate the correct button?
Credit due to Mr Bob Stanton
You have nine pearls, one of which is (as is usually the case in these problems) fake. You know that the fake pearl weighs less than the others, but it is (of course) impossible to distinguish from the others in any other way.
What is the minimum number of weighings that must be performed to find the fake pearl? How would you go about it?