This problem in geometry has been solved in no less than EIGHT ways
by a pair of students. How would you solve it? How many of their
solutions can you follow? How are they the same or different? Which
do you like best?
Age 16 to 18 Challenge Level:
Complex countdown is like normal countdown except that in addition to the usual arithmetical rules of add, subtract, multiply, divide, you are allowed to use the operations of:
Mod(z), Re(z), Im(z), Arg(z) and CC(z)
These stand for: Modulus, Real Part, Imaginary Part, Argument (measures in degrees) and Complex Conjugate.
Oh, and it also uses complex numbers. Have fun!
We can think of various scoring systems for this game; we'll leave it up to you to devise your own. You might well wish to play this collaboratively with friends and take you time to try to hit the targets exactly.
Extension: If you wish to develop your IT skills, why not try implementing a version of this game on a spreadsheet or in code? As an extra challenge you might try to implement a version in which you know that there is always an exact solution for every game played.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.