Permalink Submitted by Rinaldi on September 19, 2019

I've followed the same approach with two and three digit numbers. Here are some interesting observations after a few iterations:

* three digit numbers
is 495 the magic number for three digit numbers?
example 1 example 2
100 - 001 = 099 920 - 029 = 891
990 - 99 = 891 981 - 189 = 792 (eventually 495)
981 - 189 = 792
972 - 279 = 693
963 - 369 = 594
954 - 459 = 495
954 - 459 = 495

* Two digit numbers
For two digits the process does not "converge" to an exact result or mysterious number instead you may get caught up in a loop:
i(1) 84 - 48 = 36
(2) 63 - 36 = 27
(3) 72 - 27 = 45
(4) 54 - 45 = 09
(5) 90 - 09 = 81
(6) 81 - 18 = 63 this is the largest digit from the result of iteration (1).

Example 2:
91-19 = 72 ( largest from iteration 2 from example 1)
72 - 27 = 45
54 - 45 = 09
90 - 09 = 81
81 - 18 = 63

what about 5,6, ..., n digit numbers? Is there a way to find all the "mysterious numbers"?

## 2-digit and 3-digit number

I've followed the same approach with two and three digit numbers. Here are some interesting observations after a few iterations:

* three digit numbers

is 495 the magic number for three digit numbers?

example 1 example 2

100 - 001 = 099 920 - 029 = 891

990 - 99 = 891 981 - 189 = 792 (eventually 495)

981 - 189 = 792

972 - 279 = 693

963 - 369 = 594

954 - 459 = 495

954 - 459 = 495

* Two digit numbers

For two digits the process does not "converge" to an exact result or mysterious number instead you may get caught up in a loop:

i(1) 84 - 48 = 36

(2) 63 - 36 = 27

(3) 72 - 27 = 45

(4) 54 - 45 = 09

(5) 90 - 09 = 81

(6) 81 - 18 = 63 this is the largest digit from the result of iteration (1).

Example 2:

91-19 = 72 ( largest from iteration 2 from example 1)

72 - 27 = 45

54 - 45 = 09

90 - 09 = 81

81 - 18 = 63

what about 5,6, ..., n digit numbers? Is there a way to find all the "mysterious numbers"?