Looking at this in the vertical aspect:
To maintain the brick bond pictured you can only lay the tiles in continuous horizontal rows of either 10cm high or 5cm high tiles, the vertical joints in each row offset from the one below.
Ignoring colour, work out the total number of horizontal rows of 5cm high tiles you have that will fill 120cm width according to the quantity available. Do the same with the 10cm high tiles. Sketch all of these rows on a bit of paper and assign each row a number. Write down each row number on a separate bit of paper, screw them all up and ask a STW member to draw them out of a hat helmet. The order you pick them out in will define the sequence of 5cm/ 10cm rows vertically.
Your 10cm high rows will be all red colour.
Mark each white and blue physical tile with an individual number, then write these numbers on separate bits of paper, and perform hat selection again to get the white/ blue colour sequence in the 5cm high rows.
QED
Of course if you don’t have to tile to the edges, then the above is a lot of tosh, but then your floor will not be completely tiled.