+0

0
32
1

Thea has a key on her calculator marked $\textcolor{blue}{\bf\circledast}$. If an integer is displayed, pressing the $\textcolor{blue}{\bf\circledast}$ key chops off the first digit and moves it to the end. For example, if $6138$ is on the screen, then pressing the $\textcolor{blue}{\bf\circledast}$ key changes the display to $1386$. Thea enters a positive integer into her calculator, then squares it, then presses the $\textcolor{blue}{\bf\circledast}$ key, then squares the result, then presses the $\textcolor{blue}{\bf\circledast}$ key again. After all these steps, the calculator displays $243$. What number did Thea originally enter?

FYI: I saw the same question on a different page.  I put in that answer but it was wrong.

May 27, 2023

#1
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1 - 243 - reverse the digits at both ends

2 - It becomes: 324

3 - Take its square root.

4 - sqrt(324) ==18 - reverse the two digits and it becomes: 81

5 - Take its square root.

6 - Sqrt(81) ==9 - the original number that Thea entered into her calculator.

May 27, 2023