Re: A puzzle
Re: A puzzle
- Subject: Re: A puzzle
- From: "Nigel Garvey" <email@hidden>
- Date: Sat, 22 Nov 2008 01:24:13 +0000
"Mark J. Reed" wrote on Fri, 21 Nov 2008 12:32:45 -0500:
>The answer isn't 100,000, unless the question is "how many times is
>the last digit a 1?".
>
>If the question is "how many 1's show up over the course of a million
>miles?", the answer is 600,000: 100,000 per digit.
On my car, and in my understanding of English, the 1 on the left shows up
just once -- at 100000 miles (as it did recently!) -- then hangs around for
another 100000 miles, after which it isn't seen again. The second 1 along
shows up ten times as often, hanging around for a tenth of the time each
time. The third shows up ten times as often as that, and so on.
(10 ^ 0) + (10 ^ 1) + (10 ^ 2) + (10 ^ 3) + (10 ^ 4) + (10 ^5)
= 111111
Or: a number made up of the same number of ones as there are digits on
the instrument.
>If the question is "how many miles does the car drive with a 1 showing
>on the odometer?", the answer is 468,559. Much harder to calculate
>without brute force counting.
It's rather a vague question, isn't it? ;)
NG
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