Challenge Level

Where should you start, if you want to finish back where you started?

Alison chose a two-digit number, divided it by $2$, multiplied the answer by $9$, and then reversed the digits.

Her answer was the same as her original number!

Then she chose another two-digit number, added $1$, divided the answer by $2$, and then reversed the digits.

Again, her answer was the same as her original number!

Charlie chose a two-digit number, subtracted $2$, divided the answer by $2$, and then reversed the digits.

His answer was the same as his original number!

Choose a number, subtract $10$, divide by $2$ and reverse the digits.

Choose a 3-digit number where the last two digits sum to the first (e.g. $615$).

Rotate the digits one place, so the first digit becomes the last (so for the example, we get $156$).

Subtract the smallest number from the largest and divide by $9$ (which is always possible).