Question

In the World of Numbers, there are many number-machines, which work in the following way: the machine
adds the two beginning digits of the number and replaces them by their sum. For example, beginning with
the number 87312 and using six such machines we obtain:
87312 — > 15312 — > 6312 — > 912 — > 102 — > 12 — > 3
How many such machines should be used in order to get the number 9...9 from the number 9...9 ?

Answer 1

Answer:

Let be the time needed for 1 machine to complete the job, so rate of one machine is (rate is the reciprocal of time) --> rate of 6 machines would be .

As --> --> days needed for 1 machine to complete the job.

To complete the job in 8 days machines are needed.

it is just an example

Difference: 9-6=3.