“A Magic Circle of Cubes”

kaprekar circle of cubes

Reading this circle clockwise produces the numbers 04, 20, 34, 12, 50, 42, 03, 41, 53, 15, 31, 25.

Reading it counterclockwise gives 05, 21, 35, 13, 51, 43, 02, 40, 52, 14, 30, 24.

The sum of the first group equals that of the second, and this holds true if the numbers are squared or cubed. Further, if the numbers in the first group are arranged in ascending order and those in the second in descending, then:

kaprekar circle sums

(Devised by D.R. Kaprekar in 1956.)