Category Archives: Mind-blowing Math Facts & Paradoxes

Did you know Alice in Wonderland is all about math?

You may know that Alice’s Adventures in Wonderland was written by Lewis Carroll, but did you know that his real name was Charles Dodgson and that he was also a mathematician?  Many mathematical concepts can be found in Alice’s Adventures in Wonderland if you look for them, and some have suggested the novel was written as a satire on the new modern mathematics emerging in the mid-19th century.

Read more in these articles at:

io9 – A Math-Free Guide to the Math of Alice in Wonderland

New Scientist – Alice’s adventures in algebra: Wonderland solved

Special Numbers: 6174

Try this:

  1. Take any four-digit number, using at least two different digits. Repdigits, such as 1111, will not work, because you will just end up with 0 after step 3.
  2. Arrange the digits in ascending and then in descending order, adding leading zeros if necessary. Add leading zeros if necessary – for example, 4560 in ascending order is 0456 and 6540.
  3. Subtract the smaller number from the bigger number.
  4. Go back to step 2 and repeat the process.

This process, known as the Kaprekar routine, will always reach the number 6174, within 7 iterations. Once 6174 is reached, the process will continue yielding 6174 because 7641 – 1467 = 6174.

For example, choose 6532:

6532 – 2356 = 4176

7641 – 1467 = 6174

Another example, choose 4905:

9640 – 0469 = 9171

9711 – 1179 = 8532

8532 – 2358 = 6174

7641 – 1467 = 6174

6174 is known as Kaprekar’s constant, named after Indian mathematician D. R. Kaprekar.