When W.G. invited us to his party he rewired the buttons' panel in the elevator and placed next to it a note:

Welcome.

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?

**
**

** -x--x-11--x-
-8-16--9--x-
-6--x--x--4-
-x--x-14--2-
**

**
**
* Credit due to Mr Bob Stanton*

Place six points around a circle of circumference 27 such that every integral distance from 1 to 26 is represented as the circumferential distance between two of these points.