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.
Full Version: Crazy Eights
Easy - I think.
(Don't drive like my brother.)
(Don't drive like my brother.)
Since the 8 can appear in each of the positions, I think it is 111,111,111
QUOTE (rcline46 @ Oct 29 2008, 09:47 AM) 
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
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.
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)
Took me a minute to figure out the answer.... took me another four to figure out why it was right.
QUOTE (Andy the Actuary @ Oct 29 2008, 09:58 AM)
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)
QUOTE (Andy the Actuary @ Oct 29 2008, 05:03 AM)
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.
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.
QUOTE (mphs77 @ Oct 29 2008, 11:04 AM)
QUOTE (Andy the Actuary @ Oct 29 2008, 05:03 AM)
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.
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.
Isn't Deuteronomy a cat? I'm pretty sure Numbers is not, however. 
(What do you expect from a non-actuary--numbers...er, deuteronomy?)
(What do you expect from a non-actuary--numbers...er, deuteronomy?)QUOTE (Andy the Actuary @ Oct 29 2008, 09:13 AM)
QUOTE (mphs77 @ Oct 29 2008, 11:04 AM)
QUOTE (Andy the Actuary @ Oct 29 2008, 05:03 AM)
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.
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.
QUOTE
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.
QUOTE (Andy the Actuary @ Oct 29 2008, 12:03 PM)
QUOTE
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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