## 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 \(2101\).

**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!)

## Resources

## Books

Take your understanding to the next level with easy to understand books by James Tanton.

BROWSE BOOKS

## Guides & Solutions

Dive deeper into key topics through detailed, easy to follow guides and solution sets.

BROWSE GUIDES

## Donations

Consider supporting G'Day Math! with a donation, of any amount.

Your support is so much appreciated and enables the continued creation of great course content. Thanks!

## Ready to Help?

Donations can be made via PayPal and major credit cards. A PayPal account is not required. Many thanks!

DONATE