Magic 11

1
Magic 11 (developed from work by Mrs. D Adams
AST, Cedars School, Leighton Buzzard) Take any
two digit number (the two digits should be
different). Write down the different
arrangements of the digits. Add them up. Divide
this total by the sum of the two digits. e.g.
34 43 77 3 4 7 77 7 11 What
do you notice? Try again with a different two
digit number. Why does this happen? Extend this
by looking at three digits, four digits, is there
a way to predict the results? Can you find a
general formula? What happens if you have
repeated digits? HINT A two digits number
can be written as ab, where a and b are not
being multiplied but are positioned in the tens
and units columns respectively. This number ab
can then also be rewritten using the normal
algebra rules as 10a b