Try to know the answer for this one ;)(adsbygoogle = window.adsbygoogle || []).push({});

POW = Problem of the Week

In this POW , you are to investigate a certain rule for generating a sequence of numbers. The rule involves the repeated use of a three-step arithmetic process.

The following example shows this three-step process works if you start with the number 473.

Step 1. Arrange the digits from largest to smallest:743

Step 2. Arrange the digits from smallest to largest:347

Step 3. Subtract the smaller number from the larger one

743

-347

_____

396 The result of subraction,396, is called the high-low difference for the original number 473.

(The name comes from the fact that 743 is the highest number you can get from the digits of the number 473, and 347 is the lowest.)

You can then take 396 and find its high-low difference, and then take that number and find its high-low difference, and so on. We will call the numbers you get in this manner the high-low sequence for the starting number 473.

Your TASK in this POW is to investigate these sequences for various starting numbers. You should continue with each high-low sequence until something interesting happens.

Begin by investigating three-digit starting numbers (such as 473). Look for patterns in the high-low sequence and for reasons that explain what you see explaining.

Then see what happens with four digit numbers, five -digit numbers and so forth.

Your assignment has two components.

Figure out as much as you can about high-low differences and high-low sequences.

Explain as much of what you discover as you can.

Solve it good luck :)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Problem of the week (a memory refresher)

**Physics Forums | Science Articles, Homework Help, Discussion**