Add new comment
-
Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.
Teo tells us about his work in artificial intelligence, his travels around the world, and how inspiration sometimes strikes in the pub.
Clouds make the weather, yet their detail isn't taken into account in weather forecasts. Artificial intelligence might be able to help.
Predicting the weather is hard. With more data and computing power becoming available, artificial intelligence can help.
How does your phone know what the weather's going to be like?
How a little insect can cause chaos.
Let's omit the first stage of Kaprekar's algorithm and just look at what happens when the only rearrangement is reversing the digits in three of the numbers he looks at and doing a repeated operation.
Find the absolute difference between a number and its reverse, and then the difference between that and its reverse, and so on.
2005, 2997, 4995, 999
1789, 8082, 5274, 549, 396, 297, 495, 99
6174, 1458, 7083, 3276, 3447, 3996, 2997, 4995, 999
The absolute difference between the reverses of these repnines gives us our kernel, which is zero. That's true of all palindromes of course, though the operation in the algorithm producing a palindrome won't necessarily lead to a kernel. For example, consider summing them instead
2005, 7007
1789, 11660, 18271, 35552, 61105, 111221, 233332
6174, 10890, 20691, 40293, 79497
Lastly standard number line subtraction:
2005 ... (17 steps!) ... -8939779398
1789, -8082, -10890, -20691, -40293, -79497
6174, 1458, -7083, -10890, -20691, -40293, -79497 (A negative number can be regarded as a palindrome, eg -121 = 0-121-0)
Look at 6174 still behaving mysteriously, what's more in cahoots with that other notorious number 1089.
2005, 7007