## Exploding Dots

### 1.6 Solutions

As promised, here are my solutions to the questions posed.

1. a) Here’s how the code appears from thirteen dots.

b) The number fifty has code $$110010$$.

2. Assuming we want to make the agreement that we’ll always choose to explode dots if we can, then the code $$100211$$ is not complete: the two dots in the third-to-last box can explode to give a final code of $$101011$$.

3. This is the code for the number nineteen. (Well see next lesson a swift way to see this.)

4. a) Do it! b) Do this one too!  c) You’re on a roll. Do this third one as well!

5. Again, if we agree to do all the explosions we can, then this code is not complete: three of the dots in the second-to-last box can explode to give $$2111$$.

6. The number thirty-five has this code.

7. “Four dots in any one box explode and a replaced by one dot one place to the left.” The number thirteen has code $$31$$ in a $$1 \leftarrow 4$$ machine.

8. $$23$$

9. $$14$$

10. $$22$$

11. $$22$$ (Same code as the previous answer – but, of course, the interpretation of the code is different.)

12. a) $$13$$   b) $$37$$   c) $$5846$$  (These are the codes we use for numbers in everyday life!)

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