** Task 1:** Prove that this always works...that regardless of the 3-digit number, the final quotient magically is always 22.
** Task 2:** Generalize the trick to using 4-digit numbers, but still using it to make 2-digit numbers. What is the magic quotient now?

** Task 3:** Generalize the trick to using 4-digit numbers, but now using it to make 3-digit numbers. What is the magic quotient now?

** Task 4:** Generalize the trick to using 4-digit numbers, but using it to make both 2-digit numbers and 3-digit numbers. What is the magic quotient now?

** Task 5:** Generalize the trick to using n-digit numbers, explore different options of just 2-digit numbers, just 3-digit numbers....just (n-1)-digit numbers (or even their combinations). Does the trick still work with a predictable magic quotient?

Source: Adapted from B. Sones & R. Sones' "Math Acrobatics," *Bellingham Herald*, 1/24/2013

**Hint:** Fisrt try the trick with several different 30-digit numbers.

Second, try the trick with the three digit number, which can be written like xyz, or more properly as 100x+10y+z.

With a little algebra, the "magic" underlying the predictable quotient of 22 should become clear...

**Solution Commentary:** Some interesting numbers you should discover along the way in generalizing this magical trick: 22, 33, 666, etc.