Thea has a key on her calculator marked blue star. If an integer is displayed, pressing the  blue star key chops off the first digit and moves it to the end. For example, if  6138 is on the screen, then pressing the  blue star key changes the display to 1386.


Thea enters a positive integer into her calculator, then squares it, then presses the  blue star key, then squares the result, then presses the  blue star key again. After all these steps, the calculator displays 1372. What number did Thea originally enter?

 Nov 27, 2020

Working backwards


1372   was  3721   before she pressed the blue star key  the last time


Taking the square root of this produces    61


61   must have  been 16  before pressing  the blue star the first time


Taking the square root  of  16   = 


4 =  the original  integer



cool cool cool

 Nov 27, 2020

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