One button at a time

The nearer one wins

Press U8 and U6 together. U8 joins its point of the chain to 3V3, four resistors from BTNS. U6 joins a point further along to 3V3 as well. But the point where U8 is already sits at 3V3, and U6's point is joined to it only through R13, with 3V3 at both ends. No current flows through R13, so U6 changes nothing. BTNS reads a fifth of 3V3, exactly as for U8 alone.

The same holds for any pair, and for three or more: whichever pressed button is nearest BTNS holds its point at 3V3, and everything beyond it is shut out. In order, from the button that beats all the others to the one that beats none:

U11, U10, U5, U7, U8, U6.

Not a sketch problem

The reading with U8 and U6 held is the same number as U8 alone, to the millivolt. There is nothing left in it for a sketch to find, so no clever code can recover the second button. That is the price of six buttons on one pin, and the reason a game pad with a diagonal on its buttons needs a pin per button.

In practice it costs less than it sounds:

• Use the stick for anything that moves in two directions at once. X and Y are separate pins and read together.
• Use KEY as the second button. It is its own digital pin, so a click reads alongside anything on BTNS.
• Give U11 a job that is never combined with another press, because while it is held no other button reads at all.

Steering a dot is laid out that way: the stick moves, the diamond nudges one step at a time, KEY drops a mark, and U11 starts again.