I have a super old fashioned step counter that looks something like this:
Every time you press the button, the right hand digit increments. When this digit reaches 9 then it resets to 0 and the digit in the 10's box increments and so on. The maximum number of steps that this device can count is 9999.
The black knob on the side is how you reset the counter. When you turn it until it clicks, the lowest digit in any position increments by 1. If two or more digits match in any position they also increment. So if the black knob was turned one click on the above image the counter would read
1 3 4 1.
However, if the button was pressed another couple of times so that the display would read
2 3 5 1, and the knob was turned another click, the display would read
3 3 5 1 because the mechanical arrangement of the gears will not increment the 1 until the next full rotation. That means that the 1 will only be picked up if you rotate the knob through 8 clicks. The process would look like this:
2 2 5 1 3 3 5 1 4 4 5 1 5 5 5 1 6 6 6 1 7 7 7 1 8 8 8 1 9 9 9 1 0 0 0 1 1 1 1 1 *8 clicks* 0 0 0 0
The counter is considered reset when all 4 numbers are 0.
My puzzle is as follows:
There's a robot called Steve whose job it is to reset these counters. Steve will accept a counter and start turning the reset knob until the display reads
0 0 0 0. You may tell Steve to stop rotating the reset knob and take the counter back at any time.
The counter starts on
1 3 4 0. You can rotate the reset knob as many times as you like, however you can only press the button on the counter a total of 10 times, before Steve will no longer accept the counter back because you're deliberately screwing with him. What's the optimal method to waste Steve's time by making him turn the reset knob the maximum number of times.