## 1998-04 Solution

- Pick a number from 1 through 9.
- Let's call this number k and keep track, algebraicly, of what the results are.
- Subtract 5 from the number (negative results are ok)
- k - 5
- Multiply the result by 3.
- 3k - 15
- Square the result.
- 9k
^{2} - 90k + 225 = 9 (k^{2} - 10k + 25)
- Add the digits of the result until there's only one digit. (Example: 64. 6+4=10. 1+0=1.)
- This is the same as taking the previous result mod 9. But the previous result was divisible by 9 so here we either have 0 or 9, regardless of what k was.
- If the result is less than 5, add 5; if not, subtract 4.
- If 0 we get 5, and if it was 9 we get 5, so we have 5 here.
- Multiply the result by 2.
- 10
- Subtract 6 from the result.
- 4
- Locate the corresponding letter in the alphabet. (Examples: 1=A, 2=B.)
- d
- Pick a country that begins with that letter.
- Most people pick
*Denmark*, but other options include *Dominican Republic*
- Note the second letter in that country's name. Think of a mammal that begins with that letter.
- If Denmark, E, so we could choose
*elephant* or *emu*. If Dominican Republic, O, so orangutan or octopus.
- Now think of the color of that mammal. What do you have?
- Most will have chosen a grey elephant from Denmark.

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