## Exploding Dots

### 2.6 Solutions

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

1. Here are the values of a single dot in each of a few more boxes.

Care to keep going?

2. Thirty-seven.

3. $$11001000$$

4. a)  Each dot in the next box to the left is worth three $$81$$s, that’s $$243$$.

b) Yes it is okay to insert a zero at the front of the code. This would say that there are no $$27$$s, which is absolutely correct. Deleting the end zero at the right, however, is problematic. $$120$$ is the code for fifteen (one $$9$$and two $$3$$s) but $$12$$ is the code for five (one $$3$$ and two $$1$$s).

c) One hundred and ninety one. (Two $$81$$s, one $$27$$, and two $$1$$s.)

d) $$21102$$

5. a) For a $$1 \leftarrow 4$$ machine, boxes have the following values:

b) The number twenty-nine has code $$131$$ in a $$1 \leftarrow 4$$.

c) Thirty. (This is one more than the code for twenty-nine!)

6. Might Martians use base twelve? This means they will need twelve different symbols for writing numbers.

By the way, have you noticed that we use ten different symbols  –  $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, $$9$$, and $$0$$- which we call digits. (We call our fingers digits too!)

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