Andy the Actuary Posted October 29, 2008 Posted October 29, 2008 In the range 0-999,999,999 [one billion numbers], how many times does the number 8 appear? Count each occurrence. For example, the number 8,088 counts as 3 rather than 1. This was inspired by a recent Car-Talk puzzler. "Click and Clack" can explain everything other than why my car radio is always tuned to a hip-hop station after it is returned by the parking lot attendant. The material provided and the opinions expressed in this post are for general informational purposes only and should not be used or relied upon as the basis for any action or inaction. You should obtain appropriate tax, legal, or other professional advice.
Guest DFerrare Posted October 29, 2008 Posted October 29, 2008 Easy - I think. (Don't drive like my brother.)
rcline46 Posted October 29, 2008 Posted October 29, 2008 Since the 8 can appear in each of the positions, I think it is 111,111,111
Andy the Actuary Posted October 29, 2008 Author Posted October 29, 2008 Since the 8 can appear in each of the positions, I think it is 111,111,111 You can set up a count, for 0-9 it's 1; for 0-99 it's 20*; for 0-999, it's 300; . . .; for 0-999,999, it's 600,000. The sequence appears to emerge as n x 10(n-1), where n= number of places *8,18,28,38,48,58,68,78,80,81,82,83,84,85,86,87,88,89,98; note, 88 counts as 2 The material provided and the opinions expressed in this post are for general informational purposes only and should not be used or relied upon as the basis for any action or inaction. You should obtain appropriate tax, legal, or other professional advice.
masteff Posted October 29, 2008 Posted October 29, 2008 So I'm guessing that 42 doesn't work in this instance. Took me a minute to figure out the answer.... took me another four to figure out why it was right. n x 10(n-1), where n= number of places Alternatively, using a frequency based approach... 8 appears in 1/10 of all numbers, so number of places * number of values * 1/10 2 * 100 * 1/10 = 20 3 * 1,000 * 1/10 = 300 . . 9 * 1,000,000,000 * 1/10 = 900,000,000 Which is mathematically identical... n * 10^n * 10^-1 = n * 10^(n-1) Kurt Vonnegut: 'To be is to do'-Socrates 'To do is to be'-Jean-Paul Sartre 'Do be do be do'-Frank Sinatra
mphs77 Posted October 29, 2008 Posted October 29, 2008 In the range 0-999,999,999 [one billion numbers], how many times does the number 8 appear? Count each occurrence. For example, the number 8,088 counts as 3 rather than 1.This was inspired by a recent Car-Talk puzzler. "Click and Clack" can explain everything other than why my car radio is always tuned to a hip-hop station after it is returned by the parking lot attendant. You forgot to specify that the range is limited to integers, so using real numbers (integers plus fractions), the answers is an infinite number of occurances. Sorry, I had to be a stickler on this one.
Andy the Actuary Posted October 29, 2008 Author Posted October 29, 2008 In the range 0-999,999,999 [one billion numbers], how many times does the number 8 appear? Count each occurrence. For example, the number 8,088 counts as 3 rather than 1.This was inspired by a recent Car-Talk puzzler. "Click and Clack" can explain everything other than why my car radio is always tuned to a hip-hop station after it is returned by the parking lot attendant. You forgot to specify that the range is limited to integers, so using real numbers (integers plus fractions), the answers is an infinite number of occurances. Sorry, I had to be a stickler on this one. Okay, Yankee. Restrict to non-negative integers. Exclude imaginery, irrational, transcendental, various and sundry numbers as well as deuteronomy. The material provided and the opinions expressed in this post are for general informational purposes only and should not be used or relied upon as the basis for any action or inaction. You should obtain appropriate tax, legal, or other professional advice.
Guest Sieve Posted October 29, 2008 Posted October 29, 2008 Isn't Deuteronomy a cat? I'm pretty sure Numbers is not, however. (What do you expect from a non-actuary--numbers...er, deuteronomy?)
mphs77 Posted October 29, 2008 Posted October 29, 2008 In the range 0-999,999,999 [one billion numbers], how many times does the number 8 appear? Count each occurrence. For example, the number 8,088 counts as 3 rather than 1.This was inspired by a recent Car-Talk puzzler. "Click and Clack" can explain everything other than why my car radio is always tuned to a hip-hop station after it is returned by the parking lot attendant. You forgot to specify that the range is limited to integers, so using real numbers (integers plus fractions), the answers is an infinite number of occurances. Sorry, I had to be a stickler on this one. Okay, Yankee. Restrict to non-negative integers. Exclude imaginery, irrational, transcendental, various and sundry numbers as well as deuteronomy. Sorry Andrew, but where I am from to call someone a Yankee is an insult of quite some magnitude. I'm afraid I will have to challenge you to a duel.....water pistols at 10 paces.
Andy the Actuary Posted October 29, 2008 Author Posted October 29, 2008 I'm afraid I will have to challenge you to a duel.....water pistols at 10 paces. You are in deep trouble as I used to belong to a wter pistol club. We used to drink 'til 12 and pistol too. The material provided and the opinions expressed in this post are for general informational purposes only and should not be used or relied upon as the basis for any action or inaction. You should obtain appropriate tax, legal, or other professional advice.
mphs77 Posted October 29, 2008 Posted October 29, 2008 I'm afraid I will have to challenge you to a duel.....water pistols at 10 paces. You are in deep trouble as I used to belong to a wter pistol club. We used to drink 'til 12 and pistol too. 12 AM or 12 PM? And as for playing with your pistols...we'll just leave that one alone. This is after all a family blog.
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