2 to 1 Machine

Number Theory Level 2

The $1 \leftarrow 2$ machine:

The dots initially go into the right most box.
Whenever there are two (or more) dots are in the same box, then two dots will explode and become one dot on box to the left, unless there is no box one place to the left.

Put 13 dots into the right most box of a $1\leftarrow2$ machine. In the final display, what is the number of dots in these boxes?

1101 1111 1011 1001

3 solutions

Siva Budaraju
Jul 6, 2017

This "machine" just converts base 10 to binary. The binary representation of 13 is 1101 .

Peter Michael
Jul 6, 2017

1 dot $\rightarrow$ $\color{#69047E}{\boxed{0001}}$

2 dots $\rightarrow$ $\color{#69047E}{\boxed{0010}}$

3 dots $\rightarrow$ $\color{#69047E}{\boxed{0011}}$

4 dots $\rightarrow$ $\color{#69047E}{\boxed{0100}}$

5 dots $\rightarrow$ $\color{#69047E}{\boxed{0101}}$

6 dots $\rightarrow$ $\color{#69047E}{\boxed{0110}}$

7 dots $\rightarrow$ $\color{#69047E}{\boxed{0111}}$

8 dots $\rightarrow$ $\color{#69047E}{\boxed{1000}}$

9 dots $\rightarrow$ $\color{#69047E}{\boxed{1001}}$

10 dots $\rightarrow$ $\color{#69047E}{\boxed{1010}}$

11 dots $\rightarrow$ $\color{#69047E}{\boxed{1011}}$

12 dots $\rightarrow$ $\color{#69047E}{\boxed{1100}}$

13 dots $\rightarrow$ $\color{#20A900}{\boxed{1101}}$

Given that you are trying to convey the idea of there being 4 boxes, I feel that your solution should contain 4 boxes for each number of dots.

Jonathan Quarrie - 3 years, 11 months ago

I will edit my solution like you showed with the way you formatted your $LaTeX$ . Thank you for your example and feedback! Long way to go on improving the quality of these questions... I am aware.

Peter Michael - 3 years, 11 months ago

Jason Nguyen
Jan 14, 2018

the only way to do this is hard core visualization :octocat:

2 to 1 Machine

3 solutions

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