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### Which Car is in the Pole Position?

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Date: 08/14/99 at 14:01:12
From: Gregory Marcelin

The 10 cars entered in the Rithmetic Road Rally are lined up in their
starting positions. Which car is in the pole position (the first car)?
Use nine of the digits 0 through 9 one time each, plus the clues
below, to help you write the correct number on each car. The digit
that is not used is the number of the first car.

Hint: Cross out each digit as you write it on a car:

0 1 2 3 4 5 6 7 8 9.

Here are the 10 cars lined up:

Car1, Car2, Car3, Car4, Car5, Car6, Car7, Car8, Car9, Car10

CLUES:
1. The thousands digit is larger than any digit in the millions
period.
2. The hundreds digit plus the ones digit equals the tens digit.
3. The hundred thousands digit is the largest one.
4. The hundred millions digit plus the ten millions digit equals the
millions digit.
5. The number is even.
6. 0 is beside 9
7. The hundred millions digit is even.
8. The digits on the last three cars are the three smallest prime
numbers.
```

```
Date: 08/18/99 at 10:16:25
From: Doctor Rick

Hi, Gregory. It's hard to find a way to help you without just giving

If I understand the question correctly, the cars are lined up so that
the cars that aren't in pole position form a nine-digit number:

__ __ __, __ __ __, __ __ __

Car "10" is really car 0. You need to start by finding some clues that
tell you the most, so you can fill in at least one digit to start
with. Then you can use that digit, and the fact that other digits
can't be the same, to help figure out another digit, and so forth. It
isn't easy.

I started with clues 5, 8, and 2. What does clue 5 tell you about one
digit? What 3 numbers does clue 8 refer to? Which of these numbers
fits clue 5? Finally, how does clue 2 tell you where the other 2
numbers belong?

After that, you're on your own. I'll just point out that clue 3 gives
you 2 possibilities, but clue 6 narrows it down. How?

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```
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