Amazing 9
Thanks
S Froggatt
Effect
Every student writes down
their telephone number (without area code) or any number of as many
digits.
Now shuffle these digits around to make a smaller
number.
Example
: 6358 can be shuffled to make
3865.
The
more digits in their number, the better!
Now
subtract the small
number from the big number and tell them to keep the answer to
themselves.
Now highlight
any digit (not
a 0) in their answer.
Add up
all the other
digits:
3 4
1 6 2 2 9
=> 3+1+6+2+2+9 = 23
Now
go around the class,
asking for
the final answers and IMMEDIATELY tell the pupils which number
they highlighted :
Answer
= “23”
“You highlighted "4”
Method
One of the most incredible
properties
of our number system is its power to make tricky calculations very
easy.
Since we write our numbers in base 10, it follows that when we
subtract the digits from a number we always end up with a multiple of
9.
(This is basically saying that 1000 – 1 and 100 – 1
and
10 –
1 are all multiples of 9.)
One
of the properties of any
multiple
of 9 is that its digital root (the sum of its digits, with the
addition repeated until a single digit is reached) is also 9.
Putting
these two together
we can see
that the answer to the subtraction is always going to be a multiple
of nine.
All you have to do is answer back with the smallest number
that will make their total up to a multiple of 9.
If it is already a
multiple of 9, then they must have crossed out 0 or 9, but zero was
forbidden, therefore 9 is the answer.
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Math Tricks
