Problems Section: Problems 1361 - 1370

Q1361 Find a six digit number which can be split into three two digit squares and also into two three digit squares.  (The first digit of a number cannot be zero.)
Q1362 Sandy leans a ladder against a wall in order to clean the gutter running along the top of the wall.  Sandy is worried that the foot of the ladder is going to slip away from the wall and therefore ties a tightly stretched string between the middle of the ladder and a nail which is located directly below the top of the ladder, at the point where the floor meets the wall.  Assuming that the floor is perfectly horizontal and the wall is perfectly vertical, how much is this going to help?
Q1363 Find the smallest possible value of $x^2+y^2$, if $x$ and $y$ are real numbers for which $y\ge2+3x$ and $y\le7\sqrt x\,$.