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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 sad

 Jan 21, 2019
 #1
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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.

 Jan 21, 2019

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