This year I'm a volunteer teacher at JLS in Palo Alto to help guide a
small number of curious children into the wonders of advanced
mathematics over 12 classes in 6 weeks. The program is called "The
Number Devil". It uses chapters from the similarly named book by
Hans Magnus Enzensberger as anchor points for discussion during each
class.
Just before the holidays started, the students were to do a warm-up
exercise in preparation for diving into the deeper wonders of Number
Theory in upcoming classes. Here is the exercise, called the Four
Fours. Using exactly 4 digits, all of which are fours, and any number
of the arithmetic operators Plus, Minus, Times, Divide,
Exponentiation, Factorial, Square Root, and Parenthesis, derive each
of the numbers from 1 to 50. E.g. One way you can derive 1 is
obviously 4/4 *4/4. No doubt there are a number of different ways to
derive each number and the goal is to get students to think about
this, and to come up with expressions that are different from those of
their colleagues.
We, however, decided to turn this little exericse into a game, which
as a matter of fact, also turned out to be a good game to occupy young
minds during the holidays! Here is how you would play it:
The game has 15 rounds. Each round lasts 1 minute. We tried to cover
15 numbers in the game.
Each round consists of:
- Host (me): Calling out a different random integer between 1 and 50.
- Players: Each of them has 30 seconds to write an expression
with exactly 4 4s and the arithmetic operators to get this number.
- We compare answers and points are scored for this round as
follows:
- Zero points - No expression or invalid expression
(meaning it doesn't evaluate to the number called)
- M-N points - Otherwise. M is the number of players and N is the number of other players who have the same expression as you. If your expression is unique, you get the full M points for the round.