Take any three different digits.

1. Create every possible two-digit combination.
2. Find their sum.
3. Sum the original three digits.
4. Divide your answer from part 2 by your answer to part 3.

What number do you always get, and why?

Three numbers: x y z

1) Two-digit numbers:
xy = 10x + y
xz = 10x + z
yx = 10y + x
yz = 10y + z
zx = 10z + x
zy = 10z + y

2) SUM = 22x + 22y + 22z = 22(x + y + z)

3) Sum of the original three numbers = x + y + z

4) Divide 2) by 3) = 22(x+y+z)/(x+y+z) = 22

;-)

Posted by Bruno on 2005-12-04 12:08:55