Determine the smallest octal (base 8) perfect square which ends with 2011 (reading left to right). What are the next two smallest octal perfect squares with this property?

***For an extra challenge, solve this puzzle without using a computer program.

Broll has a much more elegant solution which accomplishes this in one fell swoop but...

You could find out what last digits have a square in octal that ends in 1 by squaring in decimal and converting to octal:  1, 5, and 7
Then for each of these find which 2 digit endings have squares ending in 11:  61, 35 and 67

This is a rather tedious process.
I stopped here but you can next find the third to the last digit so that the square ends in 011 and then the fourth to last giving 2011.

Posted by Jer on 2011-10-07 12:28:20