Age 14 to 16 Challenge Level:
For the first part, try starting with only four cards and compare
the resulting final card with the final card when you start with
Notice anything ?
What might be a good number of cards to try next ?
When you are ready to look for a general result, be systematic and
list your results, for example : seven cards and the final card is
6, eight cards and the final card is . . . , nine cards . . . .,
ten cards . . .
Remember to collect results in the other direction away
from seven cards. Six cards and the final card was . .
If you've been careful you will see a clear pattern.
First describe the pattern. Then try to account for it.