# The Guido mosaics

It is generally not known that the celebrated piece of Venetian mosaics from Domenichio, known as the Guido collection of Roman heads, was originally divided into two square groups, discovered in different periods. They were assembled to recover what is supposed to be its correct form, in 1671. Apparently, it was accidental that it was discovered that each of the squares consisted of pieces that could be joined and formed a piece larger than 5 x 5, as seen in illustration.

It is a beautiful riddle, and like many riddles, like mathematical propositions, they can be solved back and forth advantageously, we will reverse the problem and ask you to Divide the large square into the smallest possible number of pieces that can be reassembled to form two squares.

This riddle differs from the Pythagorean principle of cutting with bias lines, we know that two squares can be divided by their diagonals to produce a larger square, and vice versa, but in this riddle we must cut only by the stripes so as not to destroy the heads. Incidentally we will say that students who dominate the Pythagorean problem will not find too much difficulty in discovering how many heads there should be in the two squares that result.

Problems of this kind, which require the "best" answer with "the least possible number of pieces", offer great stimulus to intelligence. In this problem, the least solution does not destroy any of the heads or turn them upside down.

#### Solution

This riddle is based on Euclid's famous problem 47 which shows that the squares on the side and the base must be equal to the square of the hypotenuse.

Here we can see that the square of 3 plus the square of 4 is equal to the square of 5.