Thea has a key on her calculator marked x. If an integer is displayed, pressing the x key chops off the first digit and moves it to the end. For example, if 6138 is on the screen, then pressing the x key changes the display to 1386.
Thea enters a positive integer into her calculator, then squares it, then presses the x key, then squares the result, then presses the x key again. After all these steps, the calculator displays 243. What number did Thea originally enter?
This has already been answered here, but it is incorrect: https://web2.0calc.com/questions/thea-has-a-key-on-her-calculator-marked-if-an-integer
Just reverse the process by going backwards:
1 - 243 This is after she pressed the x key. So,it must have been:
2 - 324 Since 2nd last step was squaring the number, then that means we must take its square root:
3 - Square root of 324 is 18. Then she pressed the x key and this becomes:
4 - 81 - Since the first step was to square the number, that means we do the reverse by taking its square root:
5- Square root of 81 is 9.
6- 9 is the number that Thea started with:
7 - Check: 9. square it =81. press the x key and you get: 18. Square it again and you get: 324. Press the x key and you get: 243.