« Boston Python puzzles

# A Hot Date With itertools

[inspired by http://www.dgp.toronto.edu/~flaps/progprobs.html]

Consider these base-10 digits: 123456789. If you insert spaces between them, you get various sequences of numbers:

```1 2 3 4 5 6 7 8 9
12 3 4 5 67 8 9
1 2 34 5 6 7 89
12 34 56 78 9
1 23456 78 9
12345 6789
etc.
```

1) Write a program that generates all possible combinations of those digits.

How many are there?

Now let's insert a maximum of 8 addition or subtraction operators between the numbers, like this:

```1+2+3+4+5+6+7-8+9
12-3+4+5-67-8+9
1+2+34+5-6-7-89
12-34+56+78+9
1+23456-78-9
12345+6789
etc.
```

Notice that those arithmetic expressions equate to different values:

```1+2+3+4+5+6+7-8+9 = 29
12-3+4+5-67-8+9 = -48
1+2+34+5-6-7-89 = -60
12-34+56+78+9 = 121
1+23456-78-9 = 23370
12345+6789 = 19134
etc.
```

2) Write a program that generates all possible expressions in this way.

How many sum to 100?

3) Write a program that finds all such expressions for any sum.

Which sum is the most popular, i.e. has the most expressions?

4) Bonus: We can haz pretty data viz?

Like how about a histogram of the number of expressions with sums from -23456788 to 123456789. (A log scale might help. Maybe binning, too.)

## Solutions

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