Apple

On Nov 21, 2008, at 11/21 11:54 , Paul Berkowitz wrote:

On 11/21/08 7:59 AM, "Michelle Steiner" <email@hidden> wrote:

Your car odometer has 6 digits, from 000000 to 999999.

If your car made it to 1,000,000 miles, how many times would the
number 1 have shown up?

My first Applescript solution was:

set counter to 0
repeat with i from 0 to 999999
set x to i as string
if "1" is in x then
repeat with j in x
if contents of j is "1" then
set counter to counter + 1
end if
end repeat
end if
end repeat
counter

It took 63 seconds on my machine.

This cut it down to 58 seconds:

set counter to 0
repeat with i from 0 to 999999
set x to i as string
if "1" is in x then
repeat with j from 1 to length of x
if character j of x is "1" then
set counter to counter + 1
end if
end repeat
end if
end repeat
counter

They're both brute force, and I have a gut feeling that there's a more elegant method that I'm overlooking.

-- Michelle

Here's the method given on Car Talk a few weeks ago:

There are 10 digits (0-9).
All of them occur an equal number of times.
So the number 1 shows up (1,000,000 / 10) times
= 100,000

QED

--
Paul Berkowitz

References:
	>Re: A puzzle (From: Paul Berkowitz <email@hidden>)