THE UNBELIEVABLE NUMBER 6174

Take any four digit number. But one condition, all digits should not be the same like 1111 or 3333. But 2 or 3 digits can be same. Let us consider the number 2017.

STEPS
1.Arrange the digits of the number in descending order. that is , make biggest number out of four digits. We get 7210.
2. Next, arrange the digit in ascending order, making smallest number out of the same four digits. It is 0127 or 127.
3. Subtract the small number from the big one.
7210 - 127 = 7083.

Now repeat the above three steps with 7083.
1. 8730
2. 0378
3. 8730-378 = 8352
Repeat the process few more times.
2017
1. 7210-0127 = 7083
2. 8730-0378 = 8352
3. 8532-2358 = 6174
4. 7641-1467 = 6174

within 3 iterations, the result stuck at 6174. It does not change further. 6174 is called kaprekar's constant or kernel of the 4 digit numbers. The process is known as keprekar's operation.

All the 4 digit numbers end up at 6174 within 7 iterations. Now we can understand why we cannot include numbers like 3333 because small number and big number cannot be constructed using them.

I will end this articles with some open questions for your personal research.
1. What about 3 digits or 5 digits numbers etc.,?
2. Can it be applicable to numbers with other bases?
3. Any practical use for keprakar's constant? Can you devise one?
4. Can you design a operation similar to keprekar's?

Comments

Your heart -you do not know

Size and Location: The human heart is roughly the size of a clenched fist and is located slightly to the left of the center of the chest. Despite its relatively small size, the heart plays a crucial role in pumping blood throughout the entire body. Heartbeat Variability: The heart does not beat at a constant rate. The interval between heartbeats can vary, and this variability is considered a sign of a healthy heart. Factors such as breathing, emotions, and physical activity influence the heartbeat. Electrical Conduction: The heart's contractions are controlled by electrical impulses. The sinoatrial (SA) node, often called the "natural pacemaker," generates electrical signals that regulate the heartbeat and coordinate the pumping of blood. Blood Pumping Capacity: On average, the human heart pumps about 2,000 gallons (or 7,570 liters) of blood each day. Over a lifetime, this amounts to pumping enough blood to fill several Olympic-sized swimming pools. Heart Chambers and V...

THE WORK HORSE "="

One cannot think of a mathematical step without 'is equal to ' . It balances right hand side and left hand side. It aids simplification and manipulation of a mathematical expression. example: 2(A+B) = C 2A+2B = C 2A = C-2B A = C-2B/ 2 In an electronic calculator, the pressing of ' = " sign executes an asthmatic expression or simply calculates. In computer languages, it plays very important role. A = B When a computer looks at this expression, the value stored in the location named B is just transferred to the storage named A . After execution both A and B will have the same value an...

How does your smart phone detect motion, steps, rotation, and location?

How it works-1 An accelerometer in a smartphone is a microelectromechanical system (MEMS) device that measures acceleration and tilt. It works by detecting changes in motion by measuring the vibration or acceleration of the device. The accelerometer consists of a small mass suspended on a spring inside a sealed chamber. When the device is subjected to acceleration, the mass moves relative to the device, causing a change in capacitance that can be measured and processed by the smartphone's hardware. The accelerometer measures acceleration in three dimensions (x, y, and z) and provides data that the smartphone's software can use to determine the device's orientation, detect motion, and track changes in velocity and acceleration. The accelerometer is used for a variety of purposes in a smartphone, including screen rotation, motion tracking for games and fitness apps, and detecting the position of the device for navigation and location services. Additionally, it can be used t...

sciencecapsules

Search This Blog