Question 8
A special calculator has three commands (A, B and C) that can be used to modify the number that is displayed on the calculator.
The three commands are as follows:
- Command A: Insert 2 as the rightmost digit of the number.
- Command B: Replace the number with the sum of all its digits.
- Command C: Replace each digit $d$ of the number with the digit $10-d$, except that 0 is replaced with 0. (For example, 1085 would become 9025.)
For example, this is how one can arrive at 82 from 20 in 3 steps
If the calculator initially displays the number 26, show the step by step process on how to get the calculator to display 99 by using exactly six commands.
Paper instruction: Give a full solution.
The three commands are as follows:
- Command A: Insert 2 as the rightmost digit of the number.
- Command B: Replace the number with the sum of all its digits.
- Command C: Replace each digit $d$ of the number with the digit $10-d$, except that 0 is replaced with 0. (For example, 1085 would become 9025.)
For example, this is how one can arrive at 82 from 20 in 3 steps
If the calculator initially displays the number 26, show the step by step process on how to get the calculator to display 99 by using exactly six commands.
Paper instruction: Give a full solution.