Mysterious number 6174

 

Kaprekar's operation

In 1949 the mathematician D. R. Kaprekar from Devlali, India, devised a process now known as Kaprekar's operation. First choose a four digit number where the digits are not all the same (that is not 1111, 2222,...). Then rearrange the digits to get the largest and smallest numbers these digits can make. Finally, subtract the smallest number from the largest to get a new number, and carry on repeating the operation for each new number.

It is a simple operation, but Kaprekar discovered it led to a surprising result. Let's try it out, starting with the number 2005, the digits of last year. The maximum number we can make with these digits is 5200, and the minimum is 0025 or 25 (if one or more of the digits is zero, embed these in the left hand side of the minimum number). The subtractions are:

5200 - 0025 = 5175
7551 - 1557 = 5994
9954 - 4599 = 5355
5553 - 3555 = 1998
9981 - 1899 = 8082
8820 - 0288 = 8532
8532 - 2358 = 6174
7641 - 1467 = 6174

When we reach 6174 the operation repeats itself, returning 6174 every time. We call the number 6174 a kernel of this operation. So 6174 is a kernel for Kaprekar's operation, but is this as special as 6174 gets? Well not only is 6174 the only kernel for the operation, it also has one more surprise up it's sleeve. Let's try again starting with a different number, say 1789.

9871 - 1789 = 8082
8820 - 0288 = 8532
8532 - 2358 = 6174

We reached 6174 again!

Source: Mysterious number 6174

How does a rice cooker know when to turn off?

How does a rice cooker know when to turn off?

There are a number of appliances that "know" when they should turn off. A rice cooker is one of them. The water-heating portion of a drip coffee maker (as opposed to the burner under the pot) is another. Automatic hard-boiled-egg makers work the same way.

All of these appliances use the same principle. If there is water in a heated container and the water is boiling, the container will maintain a constant temperature. See How Refrigerators Work for two experiments you can perform to prove this fact to yourself.

At sea level, the boiling temperature for water is 212 degrees F or 100 degrees C. As soon as all of the liquid water has evaporated (or, in the case of the rice cooker, as soon as all of the water is absorbed by the rice), the temperature inside the container immediately rises. The appliance has a thermostat that can detect when the temperature rises above 212 degrees F in the container, and it turns itself off.

Source: Howstuffworks "How does a rice cooker know when to turn off?"