Documents

  1. Single 9-block
  2. Thirty-two 9-blocks
  3. Template for 3zees
  4. Sample Distribution
  5. Guide to Sample Stalagmite Model

Netlogo Models

  1. 9 Blocks
  2. Sample Stalagmite
  3. Sampler
  4. Sampler client

Discussions

  1. Ways of Counting
  2. Tree Counting
  3. Binary Counting
  4. Concatenation
  5. Two Square Concatenation
  6. Other Concatenations
  7. Quantity Groups
  8. Independent Events
  9. Dependent Events
  10. Calculating Probability
  11. Counting Reconsidered
  12. Probabiliy Formula
  13. Independent Events Formula
  14. Apply Independent Events Formula
  15. Stalagmite Riddle

Related Links

Binary Counting

Consider the binary numbers:

000000000
000000001
000000010
000000011
000000100
000000101
000000110
...

If we let 0 stand for a blue square and let 1 stand for a green square, then we can use these numbers to color all the 3x3 grids without redundancies.  Using the number 011010010, for example, we would color the first square blue, the next two green, the next one blue, the next two green, then a blue, then a green.

If we keep counting this way, what is the highest number we can have with 9 digits?  What does that tell us about the total number of colorings?  Don't forget that 000000000 is also a coloring.  If you need a review of binary numbers, look at the Number Bases link in the column on the left.