Thea has a key on her calculator marked *. If an integer is displayed, pressing the * key chops off the first digit and moves it to the end. For example, if 6138 is on the screen, then pressing the * key changes the display to 138.
Thea enters a positive integer into her calculator, then squares it, then presses the * key, then squares the result, then presses the * key again. After all these steps, the calculator displays 243. What number did Thea originally enter?
Also, I know this question was previously asked, but no one ever answered it
The example in your first paragraph is not consistent with the words! Assuming the example should be 6138 goes to 1386, then:
Prior to the last * the number was 324
The square root of this is 18
Prior to the first * the number was 81.
The original number was therefore the square root of this, namely, 9.