UC知道神秘的"6174"－陷阱数
来源：百度知道 编辑：UC知道 时间：2024/05/13 06:00:30
再把4176按上面方法重复一遍：7641-1467=6174
再作，奇怪的事就出现了，7641-1467＝6174；又回到了6174。
这个是偶然的吗？不，再随便举一个四位数，按上面的方法连续去做，最终那个6174还是幽灵般出现。对于任何一个数字不完全相同的四位数，最多运算7步，必然落入陷阱中
这个陷阱数已由印度数学家给出证明。
谁能提供一下证明的过程。
注意，是任意四位不完全相同的数！！！
What is the Kaprekar Number?
The number 6174 is called the Kaprekar number. The Indian mathematician D.R.Kaprekar made the following discovery in 1949.
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(1) Take a four-digit number with different digits (acbd with .a<b<c<d)..
(2) Form the largest and the smallest number from these four digits (dcba and abcd)..
(3) Find the difference of these digits. Maybe this is 6174 (dcba - abcd = 6174?).
If it is not, form the largest and the smallest number from the difference and subtract these numbers again. You may have to repeat this procedure.
The end result is always 6174, but there are no more than 7 steps.
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1st example: Take the number 1746.
1st step: 7641 - 1467 = 6174
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