desertlilac,
I made a solve of this already - so just do this:
Label the buttons - top to bottom, left to right:
1-4, 5-8, 9-12 and 13-16.
The numbers in parenthesis are the numbers of times those buttons are to be clicked.
1 (2xs), 2 (3xs), 9 (1x), 13 (1x)
1 (1x), 2 (1x), 3 (1x), 4 (2xs), 8 (1x)
1 (3xs)
11 (2xs), 12 (3xs), 15 (3xs)
16 (3xs), 12 (1x), 8 (1x), 16 (3xs)
Have fun!