Yang Hui's Magic Circles: 1 to 33 Around a Lone 9
A 13th-century Chinese mathematician placed the numbers 1 through 33 across four concentric rings around a single central number, 9. He arranged them so that every diameter — a straight line of numbers running out from the center to the opposite edge and back — adds up to exactly the same total. What was that total, and how could you place the numbers to hit it every time?
Reveal the answer
147. Every one of the four diameters running through the central 9 sums to exactly 147, one of several magic circle patterns Yang Hui published where whole rings and cross-lines all matched simultaneously. It appeared in his 1275 treatise Xugu Zhaiqi Suanfa ('Sequel to Excerpts of Mathematical Wonders'), among the earliest documented magic circles in mathematical history, centuries before the idea was studied in the West.