Choose four distinct digits and arrange them into the largest and smallest numbers possible (e.g., 9751 and 1579). Subtract the smaller from the larger to produce a new number (9751 – 1579 = 8172) and repeat the operation.

Within seven iterations you’ll always arrive at 6174.

With three-digit numbers you’ll aways arrive at 495.

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:

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

Choose any three-digit number that’s not a palindrome.

Reverse its digits, and subtract the smaller number from the larger.

Reverse the digits of this new number (prepend a zero first if it has only 2 digits) and add this time.

The result will always be 1089.

See Kaprekar’s Constant, Easy, and The Pull of Four.