TWCP OTD (The Who Cares Puzzle Of The Day) - 24th of January, 2017
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THE MOST AND LESS FREQUENT DIGITS IN THE NUMBERS FROM 1 TO 1000 It is not about writing code - but it is possible - but some nice logical explanation... So which is the most frequent digit in the list of numbers form 1 to 1000? And the less frequent? Why? And even Google is our friend - it would be nice to not to tell him about it...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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THE MOST AND LESS FREQUENT DIGITS IN THE NUMBERS FROM 1 TO 1000 It is not about writing code - but it is possible - but some nice logical explanation... So which is the most frequent digit in the list of numbers form 1 to 1000? And the less frequent? Why? And even Google is our friend - it would be nice to not to tell him about it...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
OK, I'll be the first in. 1 is the most only because you are going from 1 to 1000. If it was 1 to 999 or 2 to 1000, there would be the same number of 1's as all other non-zero numbers. 0 is the least because numbers do not start with a 0. (except 0 which is not included).
Brent
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THE MOST AND LESS FREQUENT DIGITS IN THE NUMBERS FROM 1 TO 1000 It is not about writing code - but it is possible - but some nice logical explanation... So which is the most frequent digit in the list of numbers form 1 to 1000? And the less frequent? Why? And even Google is our friend - it would be nice to not to tell him about it...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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OK, I'll be the first in. 1 is the most only because you are going from 1 to 1000. If it was 1 to 999 or 2 to 1000, there would be the same number of 1's as all other non-zero numbers. 0 is the least because numbers do not start with a 0. (except 0 which is not included).
Brent
dbrenth wrote:
1 is the most only because you are going from 1 to 1000
That does not convince me... That's a sloppy reasoning at the best...
dbrenth wrote:
0 is the least because numbers do not start with a 0.
But 1000 brings in three zeroes...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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Without thinking much: The less is obviously the zero. The most probably the one because 1000 is the only 4-digit number.
Jochen Arndt wrote:
The less is obviously the zero.
I see nothing obvious there... You may say, that the line does not start with zero so it is at least one appearance behind, but 1000 adds three more zeroes!
Jochen Arndt wrote:
The most probably the one because 1000 is the only 4-digit number.
OK. But that implies, that no other number had an advantage before than... Why is that?
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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THE MOST AND LESS FREQUENT DIGITS IN THE NUMBERS FROM 1 TO 1000 It is not about writing code - but it is possible - but some nice logical explanation... So which is the most frequent digit in the list of numbers form 1 to 1000? And the less frequent? Why? And even Google is our friend - it would be nice to not to tell him about it...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
Well, you've got 1-9, where all digits except 0 appear once. Then you've got 10-19, where 1 occurs 11 times, every other digit, including 0 now, once. Then you've got 20-29, where 2 occurs 11 times, etc. by 90-99, we have all digits in count except 0 which lags by 10 (every digit occurs twice in each set of 10 except 0 which occurs once, so you've got 10 sets, so 0 lags by 10. (every other digit in the set x0-x9 occurs 11 times). 100 - 109 - Now 0 makes up for a lost digit, but loses out again in the 1n0-1n9 (where 10 > n > 0) Ultimately, at 1000, 0 should still be the least frequent digit, and 1 gets a head start on everyone else. I think I thought that through properly, but my brain is still fried mapping XML to bizarre property fields in strange class relationships that someone else wrote and where all the rules are embedded in the business logic for creating said entity containers. :sigh: Marc
V.A.P.O.R.ware - Visual Assisted Programming / Organizational Representation Learning to code with python is like learning to swim with those little arm floaties. It gives you undeserved confidence and will eventually drown you. - DangerBunny Artificial intelligence is the only remedy for natural stupidity. - CDP1802
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THE MOST AND LESS FREQUENT DIGITS IN THE NUMBERS FROM 1 TO 1000 It is not about writing code - but it is possible - but some nice logical explanation... So which is the most frequent digit in the list of numbers form 1 to 1000? And the less frequent? Why? And even Google is our friend - it would be nice to not to tell him about it...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
We need a bit of context, here. 0. Strictly normal daily usage, 1 is the first number (and is also a article, grammatically), so it will come into most use. 1. In a supermarket, 99, because they treat their customers like ****ing idiots. 2. In a nursery school: 3, 4, or 5. 3. In a brothel, somewhere between 68 and 70 (non-inclusive). 4. Etc. Whatever "answer" you give as being absolute will have some context, but will be wrong in all the others.
I wanna be a eunuchs developer! Pass me a bread knife!
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Well, you've got 1-9, where all digits except 0 appear once. Then you've got 10-19, where 1 occurs 11 times, every other digit, including 0 now, once. Then you've got 20-29, where 2 occurs 11 times, etc. by 90-99, we have all digits in count except 0 which lags by 10 (every digit occurs twice in each set of 10 except 0 which occurs once, so you've got 10 sets, so 0 lags by 10. (every other digit in the set x0-x9 occurs 11 times). 100 - 109 - Now 0 makes up for a lost digit, but loses out again in the 1n0-1n9 (where 10 > n > 0) Ultimately, at 1000, 0 should still be the least frequent digit, and 1 gets a head start on everyone else. I think I thought that through properly, but my brain is still fried mapping XML to bizarre property fields in strange class relationships that someone else wrote and where all the rules are embedded in the business logic for creating said entity containers. :sigh: Marc
V.A.P.O.R.ware - Visual Assisted Programming / Organizational Representation Learning to code with python is like learning to swim with those little arm floaties. It gives you undeserved confidence and will eventually drown you. - DangerBunny Artificial intelligence is the only remedy for natural stupidity. - CDP1802
Not bad for an old chap Marc... The only thing is that 0 is behind by 11 in the 1-99 range, so the three zeroes of 1000 can't help it out...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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dbrenth wrote:
1 is the most only because you are going from 1 to 1000
That does not convince me... That's a sloppy reasoning at the best...
dbrenth wrote:
0 is the least because numbers do not start with a 0.
But 1000 brings in three zeroes...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
For the most, The problem actually scales down to what is the most frequent digit between 1 and 10. There are 2 ones. It is the same idea for 1 to 1 X 10^n. You wouldn't notice the least until you get to 11 to 20. In this case, 1 shoots out ahead because it leads half of the digits. in 21 to 30, 2 catches up to 1. But there is no equivalent section of numbers for 0. In 1 to 100 there are only 11 0's, which puts it far behind the other numbers and it never catches up.
Brent
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We need a bit of context, here. 0. Strictly normal daily usage, 1 is the first number (and is also a article, grammatically), so it will come into most use. 1. In a supermarket, 99, because they treat their customers like ****ing idiots. 2. In a nursery school: 3, 4, or 5. 3. In a brothel, somewhere between 68 and 70 (non-inclusive). 4. Etc. Whatever "answer" you give as being absolute will have some context, but will be wrong in all the others.
I wanna be a eunuchs developer! Pass me a bread knife!
What about the numerical context?
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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What about the numerical context?
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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For the most, The problem actually scales down to what is the most frequent digit between 1 and 10. There are 2 ones. It is the same idea for 1 to 1 X 10^n. You wouldn't notice the least until you get to 11 to 20. In this case, 1 shoots out ahead because it leads half of the digits. in 21 to 30, 2 catches up to 1. But there is no equivalent section of numbers for 0. In 1 to 100 there are only 11 0's, which puts it far behind the other numbers and it never catches up.
Brent
Now, that's much better!!! :thumbsup:
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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I wanna be a eunuchs developer! Pass me a bread knife!
You won the big prize today!!!
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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Jochen Arndt wrote:
The less is obviously the zero.
I see nothing obvious there... You may say, that the line does not start with zero so it is at least one appearance behind, but 1000 adds three more zeroes!
Jochen Arndt wrote:
The most probably the one because 1000 is the only 4-digit number.
OK. But that implies, that no other number had an advantage before than... Why is that?
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
You did not wrote "list of numbers form 0001 to 1000". So it is obvious that the zero occurs less often than other digits. 1-9: Each digit except zero occurrs once 10-99: Each digit except zero occurs 10 times (10's place) plus 9 times (1's place); zero 9 times >= 100: Zero is now present at the 10's place like the other digits but not at the 100's place.
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THE MOST AND LESS FREQUENT DIGITS IN THE NUMBERS FROM 1 TO 1000 It is not about writing code - but it is possible - but some nice logical explanation... So which is the most frequent digit in the list of numbers form 1 to 1000? And the less frequent? Why? And even Google is our friend - it would be nice to not to tell him about it...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
-
You did not wrote "list of numbers form 0001 to 1000". So it is obvious that the zero occurs less often than other digits. 1-9: Each digit except zero occurrs once 10-99: Each digit except zero occurs 10 times (10's place) plus 9 times (1's place); zero 9 times >= 100: Zero is now present at the 10's place like the other digits but not at the 100's place.
Much better - it is like the second version of some code... more robust and trustworthy... :thumbsup:
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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There's a touch of Benfield's Benford's Law about this...
Benford's law is more about observation of probability in naturally occurring number lists and it is much more a phenomenon... I tried to keep it more terrestrial...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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THE MOST AND LESS FREQUENT DIGITS IN THE NUMBERS FROM 1 TO 1000 It is not about writing code - but it is possible - but some nice logical explanation... So which is the most frequent digit in the list of numbers form 1 to 1000? And the less frequent? Why? And even Google is our friend - it would be nice to not to tell him about it...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
Real programmers start counting with 0, and logically speaking, a list of 1000 numbers would only go to 999. Using my logic: Most instances = 1 through 9 (all tied) Least instances = 0 If you did it wrong (as stated by the original message), 1 would be first (by just one instance), and 0 would still be the least used. Actual results: 1-1000 0 = 300 1 = 300 2 = 300 3 = 300 4 = 300 5 = 300 6 = 300 7 = 300 8 = 300 9 = 189 0-999 0 = 190 1 = 300 2 = 300 3 = 300 4 = 300 5 = 300 6 = 300 7 = 300 8 = 300 9 = 297
".45 ACP - because shooting twice is just silly" - JSOP, 2010
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You can never have too much ammo - unless you're swimming, or on fire. - JSOP, 2010
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When you pry the gun from my cold dead hands, be careful - the barrel will be very hot. - JSOP, 2013 -
Real programmers start counting with 0, and logically speaking, a list of 1000 numbers would only go to 999. Using my logic: Most instances = 1 through 9 (all tied) Least instances = 0 If you did it wrong (as stated by the original message), 1 would be first (by just one instance), and 0 would still be the least used. Actual results: 1-1000 0 = 300 1 = 300 2 = 300 3 = 300 4 = 300 5 = 300 6 = 300 7 = 300 8 = 300 9 = 189 0-999 0 = 190 1 = 300 2 = 300 3 = 300 4 = 300 5 = 300 6 = 300 7 = 300 8 = 300 9 = 297
".45 ACP - because shooting twice is just silly" - JSOP, 2010
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You can never have too much ammo - unless you're swimming, or on fire. - JSOP, 2010
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When you pry the gun from my cold dead hands, be careful - the barrel will be very hot. - JSOP, 2013John Simmons / outlaw programmer wrote:
Real programmers start counting with 0
And outlaw programmers keep their logic as secret... :-D
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
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THE MOST AND LESS FREQUENT DIGITS IN THE NUMBERS FROM 1 TO 1000 It is not about writing code - but it is possible - but some nice logical explanation... So which is the most frequent digit in the list of numbers form 1 to 1000? And the less frequent? Why? And even Google is our friend - it would be nice to not to tell him about it...
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
Kornfeld Eliyahu Peter wrote:
which is the most frequent digit in the list of numbers form 1 to 1000?
Assuming that those are spelling errors:
2 it the least frequent, with only one instance.
0 is the most frequent, with three instances.
Poor old 1 has only two instances in the collection {1, 2, 1000}Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...
