[This puzzle is inspired by the webpage https://apparenthorizons.com/2017/10/12/the-grue-problem-and-deep-learning/]
55 workers have got a chance to double their pay, as said by their boss. So, the boss gives them a challenge.
Every afternoon, a random worker will go to a 'game room' with a counter which can take values from 0 to 9 (both-ends inclusive), a blue button and a green button.
'Press the grue button and your pay will be doubled', the boss said, 'but press the bleen button... and your pay will stay the same forever.'
Speaking of grue and bleen, one means green and the other means blue, but which means which is random every day, and no one but the boss has any way of knowing what it means on any day.
However, the counter gives a clue. There are two switches next to the counter, one which adds one to the counter, modulo ten (A) and a 'mystery' one (M).
Here is what switch M does:
If grue means green when it is pressed, the counter will be set to zero on the next day when grue means blue.
But if grue means blue, the counter will be set to 9 on the next day when grue means green.
Each worker can press either switch next to the counter, (exclusive) or press the green or blue buttons on each visit to the 'game room'.
The workers want to double their pay as soon as possible, and NEVER press a button unless they are 100% SURE what grue and bleen mean on any day.
Question: How can the workers double their pay as soon as possible?
EDIT: For clarity, no workers have any knowledge of visits aside from their own, and the counter starts at 0.
EDIT: The counter's value is displayed next to the switches.