Why is 6174 special?
6174 is known as Kaprekar’s constant after the Indian mathematician D. R. Kaprekar. This number is notable for the following rule: Take any four-digit number, using at least two different digits (leading zeros are allowed).
How do you get Kaprekar constant?
Kaprekar constant, or 6174, is a constant that arises when we take a 4-digit integer, form the largest and smallest numbers from its digits, and then subtract these two numbers. Continuing with this process of forming and subtracting, we will always arrive at the number 6174.
How do you prove 6174?
Define T(a)=a′−a″. Show that the only integer with a four-digit decimal expansion with not all digits the same such that T(a)=a is a=6174. Let a′=¯a4a3a2a1, where a4≥a3≥a2≥a1; a″=¯a1a2a3a4.
What is the Kaprekar constant for 3 digit number?
Kaprekar Routine
| possible cycles for , 2, base- digits | |
|---|---|
| 2 | 0, 0, 9, 21, (45), (49) . |
| 3 | 0, 0, (32, 52), 184, (320, 580, 484). |
| 4 | 0, 30, 201, (126, 138) , (570, 765), (2550), (3369), (3873) . |
| 5 | 8, (48, 72), 392, (1992, 2616, 2856, 2232), (7488, 10712, 9992, 13736, 11432). |
Why is 1089 a magic number?
1089 is widely used in magic tricks because it can be “produced” from any two three-digit numbers. This allows it to be used as the basis for a Magician’s Choice. Take any three-digit number where the first and last digits differ by more than 1.
Who found this number 6174?
mathematician DR Kaprekar
6174 is known as Kaprekar’s constant as it was invented by Indian mathematician DR Kaprekar in 1949. For example, lets take the number 5432.
How do I find my Kaprekar number?
In mathematics, a Kaprekar number for a given base is a non-negative integer, the representation of whose square in that base can be split into two parts—either or both of which may include leading zeroes—that add up to the original number. For instance, 45 is a Kaprekar number, because 452 = 2025 and 20 + 25 = 45.
What is meant by Kaprekar number?
In mathematics, a natural number in a given number base is a -Kaprekar number if the representation of its square in that base can be split into two parts, where the second part has. digits, that add up to the original number. The numbers are named after D. R. Kaprekar.
What is Hardy Ramanujan Number explain in 500 words?
1729, the Hardy-Ramanujan Number, is the smallest number which can be expressed as the sum of two different cubes in two different ways. 1729 is the sum of the cubes of 10 and 9 – cube of 10 is 1000 and cube of 9 is 729; adding the two numbers results in 1729.
What is the 1089 Trick?
The mystery is this: first, take any three digit number, where the first and last digits differ by two or more and reverse the number to produce a new one. Then subtract the smaller from the larger producing another new number. If you reverse this number and this time add the two, the result will always be 1089.
What does 1089 mean?
1089 (number)
| ← 1088 1089 1090 → | |
|---|---|
| Cardinal | one thousand eighty-nine |
| Ordinal | 1089th (one thousand eighty-ninth) |
| Factorization | 32 × 112 |
| Divisors | 1, 3, 9, 11, 33, 99, 121, 363, 1089 |
What is the prime factorization of 6174?
6174 = 2*3*3*7*7*7.
Which is the special number of the Kaprekar constant?
6174 is the Kaprekar Constant. This number is special as we always get this number when following steps are followed for any four digit number such that all digits of number are not same, i.e., all four digit numbers excluding (0000, 1111, …) Sort four digits in ascending order and store result in a number “asc”.
Are there 3 digit constants in Python Kaprekar?
You hard-code a lot of special numbers: 4, 9998, 6174, 8. It would be nice to reduce the usage of such constants, and where they are necessary, clarify their purpose. The Wikipedia page mentions that there is a 3-digit Kaprekar Process; it would be nice to have code that is easily adaptable to that related problem.
What is the number 6174 in Kaprekar’s routine?
Kaprekar showed that in 4-digit case, if the initial number has at least two distinct digits, after 7 iterations this process always yield the number 6174 which is now known as the Kaprekar’s constant.
What kind of algorithm is Kaprekar’s routine?
In number theory, Kaprekar’s routine is an algorithm devised by the Indian mathematician D. R. Kaprekar which produces a sequence of numbers which either converges to a constant value or results in a repeating cycle. The algorithm is as follows: