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?
xx11x
8169x
6xx4
xx142
Credit due to Mr Bob Stanton
Label the boxes with 0 and 1 like this.
0101
1010
0101
1010
The path from 1 to 16 must alternate between 0 squares and 1 squares. Therefore, either the even numbers are on the 0's and the odd numbers are on the 1's, or the even numbers are on the 1's and the odd numbers are on the 0's.
Suppose the even numbers are on the 1's and the odd numbers are on the 0's. Then, 4, 8, 11, and 14 are correct. Then, the grid looks like this.
_ _ 11 _
8 _ _ _
_ _ _ 4
_ _ 14 _
To get from 11 to 14, the third column must be 11, 12, 13, 14. Then, the 4 is blocked from getting to the 8.
_ _ 11 _
8 _ 12 _
_ _ 13 4
_ _ 14 _
Therefore, the even numbers are on the 0's and the odd numbers are on the 1's. Then, 2, 6, 9, and 16 are correct. Then, the grid looks like this.
_ _ _ _
_ 16 9 _
6 _ _ _
_ _ _ 2
To get from 6 to 9, the third row must start 6, 7, 8.
_ _ _ _
_ 16 9 _
6 7 8 _
_ _ _ 2
Now, it is easy to see the paths from 1 to 6, and 9 to 16.
14 13 12 11
15 16 9 10
6 7 8 1
5 4 3 2
Therefore, the 15 button is the first button in the second row.

Posted by Math Man
on 20200814 16:38:19 