Put any four numbers in a row, say,
77 73 29 179.
Under the first number write the difference between it and the second number. Under the second number put the difference between it and the third. Under the third put its difference from the fourth, and under the fourth, its difference from the first. We are concerned only with absolute differences, differences that are positive. The procedure gives a new set of four numbers, like so:
77 73 29 179
04 44 150 102
Repeat the procedure as long as possible. The result is:
77 73 29 179
04 44 150 102
40 106 48 98
66 58 50 58
08 08 08 08
0 0 0 0
It is not a remarkable coincidence. This will happen with any set of 4 numbers. You will always reach 0.
Why does it always happen? I know the formal proof but I am still unable to grasp it intuitively, exactly why does it happen? Can anyone explain it in simple terms without much formalities?