495 (number)
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| Template:Numbers 100-1000 | |
| 495 | |
|---|---|
| Cardinal | Four hundred ninety-five |
| Ordinal | Four hundred ninety-fifth |
| Factorization |  |
| Binary | 111101111 |
| Hexadecimal | 1EF |
The number 495 has an interesting property. Consider the following steps:
- Take any three-digit number (with a few exceptions - see below).
- Arrange the digits in ascending and then in descending order to get two three-digit numbers, adding leading zeros if necessary.
- Subtract the smaller number from the bigger number.
- Go back to step 2.
The above operation will always reach 495 in at few steps and it stops there. Once 495 is reached, the process stops because 954 – 459 = 495.
[edit] Example
For example, choose 598:
- 985 − 589 = 396
- 963 − 369 = 594
- 954 − 459 = 495
The only three-digit numbers for which this function does not work are repdigits such as 111, which give the answer 0 after a single iteration. Three-digit numbers with two equal digits, such as 211 or 990, appear to give 99 after one iteration and thus 0 after a second iteration, but work if leading zeros are included:
- 211 – 112 = 099
- 990 – 099 = 891
- 981 – 189 = 792
- 972 – 279 = 693
- 963 – 369 = 594
- 954 − 459 = 495
Kaprekar's constant has the same property for the four-digit numbers.
[edit] References
The Mysterious 6174 revisited [1], Proof for Patera's constant
