All history students know the mystery and uncertainty that reigns regarding the details of the memorable battle that took place on October 14, 1066. This riddle deals with a curious passage in the history of that battle, a passage that has not received the attention it deserves.
The passage in question, as Professor Henry Dudeney points out, says: “Harold's men remained close together, as was their custom, and formed thirteen squares with the same number of men in each square, and alas! of the Norman who dared to enter his redoubt, for a single blow of a Saxon war ax would break his spear and penetrate his chainmail ...!
When Harold launched himself into battle, the Saxons formed a unique and powerful square, uttering the battle cries of “Ut!”, “Olicrosse!”, “Godemite!” ”.
Contemporary authorities accept that the Saxons fought in that solid formation. In "Carmen de Bello Hastingensi", a poem attributed to Guy, Bishop of Amiens, we are told that "the Saxons stood firm in a dense mass." And Henry de Huntingdon speaks of "the square as a castle, impenetrable to the Normans."
If Harold's forces were divided into thirteen squares that, when Harold himself was added, could be arranged in a single large square How many men must have been?
The riddle is so difficult that few mathematicians will solve it correctly.
Extracted from the page www.librosmaravillosos.com.
The 13 Harold squads were square with 180 men per side, adding a total of 421,200 men. With the addition of Harold, the number increases to 421,201 men, which forms a large square with 649 men per side.