How Does Magic numbers: 1089 and 6174 Work?

There are special numbers that always turn into 1089 or 6174 when you do a fun number trick, like turning your favorite toy into another one just by playing with it.

Imagine you pick any 3-digit number, say, 521. Now reverse the digits to get 125. Subtract the smaller from the bigger:

521 - 125 = 396.

Now take that result (396), reverse its digits (to make 693), and add them together:

396 + 693 = 1089.

No matter which 3-digit number you start with, as long as all the digits are different, it always turns into 1089, like a magical robot that follows rules!

This one is even cooler. Pick any 4-digit number, say, 3210. Now rearrange its digits to make the largest and smallest numbers you can:

• Largest = 3210 → 3210 (or maybe 3210 becomes 3210 if all digits are different)
• Smallest = 0123 → 123

Subtract them: 3210 - 123 = 3087. Repeat the trick with that number, keep subtracting largest from smallest, and eventually, you’ll always get 6174!

It’s like a game where no matter what you pick, the rules guide you to one special answer.