- Nim (or Nim2, where one is allowed to take away 1 or 2 stones, other Nims are possible) - the complete solution is easy: if one faces the pile with the number of stones there divisible by three, one loses given the opponent plays wisely, and wins otherwise. We established that using the recursion, an awfully useful trick.
- This led to the question, how you determine divisibility by three? The sum of digits trick helps...
Draw projections of some shapes- Split into 3 parts led to the question: can one tile the plane with these pentaminos?
Homework:
- One can tile (cover without overlaps or holes) the whole plane with the r pentaminos, for example as shown below:
Now, can you tile the whole plane with T-pentaminos? Or with y's? or z's?
- Is 198407392 divisible by 3? What about 38002978643001?
- Who wins the game of Nim3 starting with the pile of 101 stones?
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