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Problem 1

A 12 by 25 by 36 cm cereal box is lying on the floor on one of its 25 by 36 cm faces.  An ant, located at one of the bottom corners of the box, must crawl along the outside of the box to reach the opposite bottom corner.  What is the length of the shortest such path?

Problem 2

Find all 8-digit natural numbers n such that n2 ends in the same 8 digits as n.  Numbers are written in standard decimal notation, with no leading zeroes.