Please help! How to solve this Bernard's Cars Problem

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onesun0000

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Bernard, who is a genius and very wealthy, owns one thousand cars, each of which is numbered with a different natural number from 1 to 1000. He invites 1000 people to a party, and he makes each person sit in a different car so that every car is occupied. He then tells all the people who are in even numbered cars to get out of their cars. then he tells everyone with a car numbered any multiple of 3 to get out (or get in if they are already out of it). Then he tells everyone with a car numbered any multiple of 4 to get out (or get in). He continues giving these instructions until he tells the last instruction: anyone with a car numbered a multiple of 1000 should get out of the car (or get into it). After all these instructions are given which cars will be unoccupied? How many occupied cars? Why those cars?

I tried to find a pattern by using the numbers 1 - 24. I got 4 cars inside and 20 cars outside, but I still can't figure out the pattern. Please help.
 
onesun0000 said:
Bernard, who is a genius and very wealthy, owns one thousand cars, each of which is numbered with a different natural number from 1 to 1000. He invites 1000 people to a party, and he makes each person sit in a different car so that every car is occupied. He then tells all the people who are in even numbered cars to get out of their cars. then he tells everyone with a car numbered any multiple of 3 to get out (or get in if they are already out of it). Then he tells everyone with a car numbered any multiple of 4 to get out (or get in). He continues giving these instructions until he tells the last instruction: anyone with a car numbered a multiple of 1000 should get out of the car (or get into it). After all these instructions are given which cars will be unoccupied? How many occupied cars? Why those cars?

I tried to find a pattern by using the numbers 1 - 24. I got 4 cars inside and 20 cars outside, but I still can't figure out the pattern. Please help.
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How many divisors do number 6 have? - 1,2,3,6 - total 4

How many divisors do number 9 have? - 1,3,9 - total 3

How many divisors do number 16 have? - 1,2,4,8, 16 - total 5

How many divisors do number 24 have? - 1,2,3,4,6,8,12,24 - total 8

How many divisors do number 25 have? - 1,5,25 - total 3

How many divisors do 30 have? - 1,2,3,5,6,10,15,30 - total 8

How many divisors do 36 have? - 1,2,3,4,6,9,12,18,36 - total 9

Why am I asking you about number of divisors to solve this problem?

Some numbers above have even number of divisors - Some numbers above have odd number of multiples. Do you see any particular pattern there?

Think some more......
 
Last edited by a moderator:
Are we confusing the term "multiples" with the term "divisors" here?
 
LCKurtz said:
Are we confusing the term "multiples" with the term "divisors" here?
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Nope - no "we" here!

I did it all by myself. Going to the corner for 31 minutes.

I edited the post above and thanks for trying to "usurp" my guilt.......
 
But the OP clearly stated "multiples", which made me wonder what the difficulty was. :)
 
onesun0000 said:
I tried to find a pattern by using the numbers 1 - 24. I got 4 cars inside and 20 cars outside, but I still can't figure out the pattern. Please help.
Click to expand...
Can we please see your work with 24. Maybe you made some mistakes, which if pointed out then you will see a pattern, or if there is no mistake then we can help you see a pattern.
 
jelly1213 said:
can you show me the bernards car problem answer? is it perfect squares?
Click to expand...
Did you read the paper referenced in response #1?

Did you read the discussion in this thread before that response?

Can you share your work/thoughts?
 
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