Okay. Let’s now go wild.

Let’s go all the way up to a $1 \leftarrow 10$  machine and put  $273$ dots in a $1 \leftarrow 10$ machine!

What is the secret $1 \leftarrow 10$ code for the number $273$?

I thought my way through this by asking a series of questions.

Will there be any explosions? Are there any groups of ten that will explode? Certainly!

How many explosions will there be initially? Twenty-seven.

Any dots left behind? Yes. Three.

Okay. So there are twenty-seven explosions, each making one dot one place to the left, leaving three dots behind.

Any more explosions? Yes. Two more.

Any dots left behind? Seven left behind.

The $1 \leftarrow 10$ code for two hundred seventy three is… $273$. Whoa!

12. a) What is the$1 \leftarrow 10$  code for the number thirteen?

       b) What is the $1 \leftarrow 10$ code for the number thirty-seven?

       c) What is the $1 \leftarrow 10$ code for the number $5846$?

Something curious is going on!

What is the natural big question to ask?

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