Below is regular 8-by-8 chessboard. Each small square (as shown in the diagram) is considered to have a side of 1 unit, so each small square would have an area of 1 square unit.

If you wanted to form a square of 9 square units, it's a simple matter of selecting any 3-by-3 region pm the chessboard. Obviously, a similar approach works for any perfect square up to 64.

Without using any other measuring devices, how would define a square whose area is exactly 10 square units on the chessboard?

Quick update: landmark sent me the correct solution! Can anyone else get it?

Feel free to post here.

A bit difficult to describe without being able to draw lines, but you need sides that are the square root of 10 in length, so one side could start on the left edge, one unit above the bottom edge, and end on the bottom edge, three units over from the left edge. That side would be the hypotenuse of a right triangle whose other two sides were of length one and three. The other three sides would be constructed in a similar fashion.

Murf

You got it, Murf!

For those having trouble following Murf's description, here's how you construct the area of 10 square units:



You're using a right triangle with a leg of 3 and leg of 1, so the Pythagorean Theorem tells us that the hypotenuse must be the square root of 10 (3 squared + 1 squared = 9 + 1 = 10, so the hypotenuse length must be the square root of 10).

There's more details about this puzzle at the original source, including all the possible square areas which can be created on an 8-by-8 chessboard (and one that can be created in 2 different ways!): http://datagenetics.com/blog/february22019/index.html