Take any number with 4 non-repeating digits. Say 1562.
Step 1: Arrange the number in ascending and then descending order
Step 2: Subtract the smaller number from the bigger number
6521 - 1256 = 5265
Repeat the steps with your new number (the answer):
(5265 rearranged) 6552 - 2556 = 3996
(3996 rearranged) 9963 - 3699 = 6264
(6264 rearranged) 6642 - 2466 = 4176
(4176 rearranged) 7641 - 1467 = 6174
Try any 4-digit number with non-repeating digits, and you'll always get 6174.
Pretty cool, huh?
6174 is known as Kaprekar's constant. The math operation above, discovered by Indian mathematician D.R. Kaprekar, will reach 6174 after at most 7 steps (if you did more than 7 iterations, check your arithmetic).
Via
Use your equal signs more carefully, surely (5265 = 6552 - 2556 = 3996) Is not a valid equation as 5265 is not equal to 3996..
ReplyDeleteanonymous, the poster isn't insinuating 5265 = 3996; he was saying that 5265 rearranged with the greatest number at the beginning is equivalent to 6552.
ReplyDeleteYes exactly. But just to be perfectly clear, I have changed it. Thanks!
ReplyDelete7156
ReplyDelete7651-1567=6084
8640-0468=8172
8721-1278=7443
7443-3447=3996
9963-3699=6264
6642-2466=4176
7641-1467=6174
awesome stuff!
I have to agree with the first anonymous poster, If you are writing "5265 = 6552 - 2556 = 3996", the you ARE implying that 5265 IS equal to 3996, no matter what your intentions were. That is what the equality sign means.
ReplyDeleteBut the original poster have now solved the "problem" in a nice way...
I have noticed that this works so long as all 4 digits don't repeat (obviously), but even up to 3 repeating digits will produce the result of 6174. Very interesting indeed.
ReplyDelete