Problem-Solving:

Look! Up in the Sky! It's a Bird! It's a Plane!

No! It's SuperNumber: 6,174!

 

Today's Snack: Eat six raisins, one apple, seven peanuts, and four oyster crackers to celebrate our SuperNumber, 6,174. Drink water, too!

 

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Supplies:

Scratch paper and pencil

 

 

            Here is a weird, strange, odd, peculiar fact of math: the number 6,174 is ALWAYS the answer, no matter what numbers you start off with, if you follow a particular process or structure in subtraction.

 

            So 6,174 is the SUPER NUMBER that CANNOT be DEFEATED. Hunhhhh?

 

Weird? Strange? Odd? Yes. So naturally, you want to know how to do it:

 

1.      Select four different numbers from 0 to 9. Let's say you pick 7, 8, 2 and 3.

 

2.      Now arrange them to make the largest number possible. So you put the biggest number first, and the smallest number last: 8,732.

 

3.      Now we're going to do a subtraction problem. Underneath the 8,732, rearrange the numbers the opposite way, to make the SMALLEST number possible: 2,378.

 

            4. Subtract the smaller number from the larger number:

 

                                                              8,732

                                                            - 2,378

                                                              6,354

 

            5. Now rearrange THAT number again, to make it as large as possible: 6,543.

 

6. And rearrange it yet again to make it as SMALL as possible: 3,456.

 

7. Subtract again:

 

                                                              6,543

                                                            - 3,456

                                                              3,087

 

            8. Do that same process again - rearrange those four numbers into the largest number possible, and from it, subtract the smallest number possible - even if there's a zero, include it:

           

                                                              8,730

                                                            - 0,378

                                                              8,352

 

            9. And rearrange one more time into largest possible and smallest possible:

 

                                                              8,532

                                                            - 2,358

                                                   6,174

 

            . . . and what do you know! There it is! Our SUPER NUMBER!!!!

 

It took us four subtractions, in this process, to come up with 6,174.

 

Now, on scratch paper, YOU try it again, with four DIFFERENT numbers.

 

How many subtractions does it take YOU to get to our SUPER NUMBER?

 

For discussion: why on Earth do you think this works?

 

Guess what? No one really knows, but 6,174 is the only number this works with.

 

It's called Kaprekar's Mystery, because it was discovered by a mathematician named Kaprekar from India. Read more about it:

 

http://plus.maths.org/content/os/issue38/features/nishiyama/index