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Which Car is in the Pole Position?


Date: 08/14/99 at 14:01:12
From: Gregory Marcelin
Subject: Rithmetic Road Rally

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
Subject: Re: Rithmetic Road Rally

Hi, Gregory. It's hard to find a way to help you without just giving 
you answers, but I'll try.

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/   
    
Associated Topics:
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