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wu :: forums    riddles    medium (Moderators: Grimbal, Icarus, ThudnBlunder, william wu, Eigenray, SMQ, towr)    zeroless number « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: zeroless number  (Read 1695 times) Christine Full Member     Posts: 159 zeroless number   « on: Aug 19th, 2012, 1:04pm » Quote Modify What is the probability that a n-digit number will not have the digit 0 ?   Is it (9/10)^(n-1) ? IP Logged towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: zeroless number   « Reply #1 on: Aug 19th, 2012, 10:44pm » Quote Modify It is if n > 1 and you don't allow leading zeroes; it's not true for single digit numbers because there the probability is 9/10 instead of 1. IP Logged Wikipedia, Google, Mathworld, Integer sequence DB playful Junior Member meet me at the second fork in the road     Gender: Posts: 100 Re: zeroless number   « Reply #2 on: Aug 20th, 2012, 2:12pm » Quote Modify Unless I'm missing something, the exponent is n (rather than n-1). 1 digit => p = 0.9 ^ 1 2 digits => p = 0.9 ^ 2 IP Logged my favorite puzzles peoplepower Junior Member     Posts: 63 Re: zeroless number   « Reply #3 on: Aug 20th, 2012, 4:44pm » Quote Modify on Aug 20th, 2012, 2:12pm, playful wrote: Unless I'm missing something, the exponent is n (rather than n-1). 1 digit => p = 0.9 ^ 1 2 digits => p = 0.9 ^ 2 If we were counting occurrences of any other digit than 0, then you would be correct. But, as towr pointed out, if we do not have leading zeros in our number then the first digit is certainly nonzero and the remaining n-1 digits have the 1/10 probability of being zero. The exception is the convention that the single digit number zero is written 0 rather than being treated as a zero-digit number, which is why when n=1 the probability is 9/10. « Last Edit: Aug 20th, 2012, 4:44pm by peoplepower » IP Logged playful Junior Member meet me at the second fork in the road     Gender: Posts: 100 Re: zeroless number   « Reply #4 on: Aug 20th, 2012, 5:18pm » Quote Modify Ah... Yes, of course. We won't allow 07 etc. Thanks for waking me up.   IP Logged my favorite puzzles Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy => medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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