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Maths question
Brer_Rabbit (A white rabbit in a tuxedo) Started conversation Mar 20, 2002
Lucinda, just the man I need for this one. I'm annoyed by a little maths puzzle. Can you help?
The puzzle was: What percentage of all integars contain at least one instance of the digit '3'. For instance '13', '33' etc.
Someone argued that the answer is 100% but I am unsure. I think the answer may actually be technically 'undefined'. What do you think?
Maths question
Martin Harper Posted Mar 20, 2002
I reckon 100%. Proportions of infinites are funny like that...
Maths question
GTBacchus Posted Apr 3, 2002
Ooh, can I play? 
If you just look at the units digit, then 10% of integers have a '3' there. Moving to the tens digit, 10% of integers have a '3' there, less 10% of those that were already counted, so that's an additional 9%. We're up to 19% now, right? Another place over, and you add 10% less 19% of 10%, which is... uh... 8.1%. Ah, I see the pattern:
10% + 9% + 8.1% + 7.29% + . . .
= 1/10 + 9/100 + 81/1000 + 729/10000 + . . .
That's a geometric series with 9/10 as the common ratio, so its sum is just the first term divided by (1 - 9/10), which comes out to... 1. As in 100%. Yep. That's very strange.
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Maths question
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