Magical 45
The problem as originally stated in "Uncle Art's Funland," a regular feature many Sunday newspapers:
Tell a friend that you can subtract 9 numbers that total 45 from 9 numbers that also total 45 and still have a remainder totalling 45.
Source: "Uncle Arts Funland," Bellingham Herald, August 28, 2005.
Hint: Clarity is not a feature in the presentation of this problem. The "9 numbers" in both instances imply that you are to find two ninedigit numbers, each made up from all of the nine digits 1, 2,...8,9 which total (i.e. addup to) 45.
Solution Commentary: The "amazing" solution given by "Uncle Art" is:
987654321123456789=864197532
Now, why even give students such a problem? Because of the new questions it raises! Some examples:
 One solution is given...is it the only solution? How do you prove/disprove the existence of other solutions?
 Does anything interesting happen with other sequences of ndigits: abcde...rst  tsr...edcba =?, where n = 1, 2,3, 4, etc. For example, I found n=2 to be interesting in that multiple soutions can be found, all exhibiting an interesting "side" pattern.
 Are there solutions for the original problem using other interpretations of its wording? For example, suppose the original set of 9 numbers was {10,11,14,5,1,1,1,1,1}add to 45. Can you find another set of 9 numbers {a,b,c,...,i} that add to 45 and such that (10+11+14+...+1+1)  (a+b+c+...+h+i) is a number whose digits total 45? Note: This question actually provides a hint to understanding of the wording of the original problem and its suggested solution.
 What does this problem have to do with the process of casting out 9's?
 Or....
