« Boston Python puzzles

# Extreme Verbal Arithmetic

Every puzzle-lover has toyed with verbal arithmetic:

`SEND + MORE = MONEY`

This verbal equation is arithmetically satisfied by these substitutions:

```{'O':0, 'M':1, 'Y':2, 'E':5, 'N':6, 'D':7, 'R':8, 'S':9}
```

which results in this numeric equation:

```9567 + 1085 = 10652
```

But that's too easy. So let's play extreme verbal arithmetic.

Rather than just representing digits, the letters can also represent the arithmetic operators +, -, *, and /.

The goal is to find the extreme solution, the one that equates to the largest value. For example:

`HI = FLY`

There are many solutions:

```13 = 9+4
15 = 8+7
16 = 8*2
21 = 7*3
```

But what is the extreme solution?

The largest possible value for HI is 98. But there is no FLY expression that evaluates to 98. (Prove it to yourself.) So how about 97? 96? 95? Nope, FLY has too few letters for their factors. Oh! How about 81 = 9*9? Sorry, FLY can't be 9*9 since F and Y are not allowed to both be 9. Nothing works until you get to the extreme solution of 72:

```72 = 9*8
```

NOTE that the characters ** are the exponential operator. For example:

```MOON = MEAT
3**4 = 3+78 = 81
```

Note also that in Python 2, numbers starting with a zero digit are base-8: 0123 == 83. In Python 3, numbers starting with zero are syntax errors! (what do numbers starting with 0 mean in Python?) And don't forget that both / and // are division operators.

You may find the solutions to this puzzle helpful.

Find the extreme solution for the following equations.

1. TON = NOT

2. SNAP = PEA

3. EMAIL = SPAM

4. MASSACHUSETTS = MA

5. NOON = TUTORIAL

6. WOMAN = MAN = NOW

7. ABBABBA = A

8. PYTHONIC = HYPNOTIC

9. CAMBRIDGE = CODERS

10. BANISTER = PAINTER = ANGER

BONUS: What verbal arithmetic equation has the most extreme solution of all? (English dictionary words only.)

And if you've gone this deep down the rabbit hole, you may be interested to learn more about the speed of calculations in Python and about truly big numbers.

## Solutions

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