Select any 3-digit number with all digits
different from one another. Write all possible 2-digit numbers that can be
formed from the 3-digits selected earlier. Then divide their sum by the sum of
the digits in the original 3-digit number.

You should

*always*get the same answer, 22. There ought to be a big resulting “Wow!”
For example, consider the three-digit
number 365.

Take the sum of all the possible two-digit
numbers that can be formed from these three digits:

The sum of the digits of the original
number is

3 + 6 + 5 = 14.

3 + 6 + 5 = 14.

Then 308/14 = 22.

**Math behind this:**

To analyze this unusual result, we will
begin with a general representation of the number: 100x + 10y + z.

We now take the sum of all the two-digit
numbers taken from the three digits:

(10x+y)+ (10y+x) + (10x+z) + (10z+x) +
(10y+z) + (10z+y)

=10(2x+2y+2z) + (2x+2y+2z)

=11(2x+2y+2z)

=22(x+y+z)

which, when divided by the sum of the
digits, (x + y + z), is 22.

These illustrations show the value of
algebra in explaining simple arithmetic phenomena.

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