THE INCREDIBLE NINE

by

Lars Løver and Jon Roger Eidet

1)

Think of a three digit number, say 534, then subtract the reverse of its digits, 435. Can you show that the sum will always have a factor of nine?

Answeer:

100a + 10b + c - (100c + 10b + a) =

99a - 99c =

9(11a-11c)

As you can see, 9 will always be a faktor.

2)

Think of a three digit number, say 435, then subtract it with sum of digits, 435 - ( 4+3+5).

Can you show that the sum will always have a factor of nine?

Answeer:

100a + 10b + c - (a + b +c) =

99a + 9b =

9(11a + b)

Even though we didn`t ask the same question we still ended up with the same kind of answeer as in 1) ; 9 is a faktor in our answeer.

kilder:

"Mathematical games" C. Lukacs and E. Tarjan

"Tallmagi" Carl- Otto Johansen