TWCP OTD (The Who Cares Puzzle Of The Day) - 24th of January, 2017
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Consider these by the length of the number we have 4 groups. 1-9 10-99 100-999 1000-1000 In the first three groups we only need to consider the first digit, the remaining digits will have an identical number of every digit 0-9, as they cover the complete range. In the final group there is only one number, so it is trivial. Group 1 adds 1 of 1-9. Group 2 adds 10 of 1-9. Group 3 adds 100 of 1-9. Group 4 adds 1 of 1 and 3 of 0. This makes 1 the most common (by 1) and 0 the least common.
Is fascinating how one can get the right answer even from the wrong reasoning...
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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Ooh, I worked this out the easy way: count them... 14 1s and 9 0s. Easy!
In the range of 1-99 there are 20 1s alone!!!
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.
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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.
Then go on to the next one: To enter our office area, you must tap the correct four digit code on the keypad by the door. For some strange reason, the checking is implemented as pipeline: The last four digits typed must be the correct ones. So, if the correct code is 2345 and you start typing 1234 the door won't open. Then you add the 5, and the door opens. In other words: You have tested two 4-digit keystrokes by 5 keypresses. Problem 1: What is the minimal number of keypresses required to go through all 10000 possible coded? Problem 2: Describe the algorithm for generating the order of keypresses Problem 3: Prove that this is the minimal number of keypresses Problem 4: The average number of codes you have to try to find the right one is 5000. How many keypresses have you made before having tried 5000 codes? Does it depend on the order of these keypresses? (Note: I do not have the answers)
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Looks to me that everybody is wrong. There are clearly more zeros than ones. Each byte is packed with leading zeros. The ones are big-time losers. QED. :laugh:
I would like to see how it goes on base 2... ;)
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.
The easy way: I made a program and the result is: 0: 192 times 1: 301 times 2...9: 300 times. So, everyone is right :)
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I would like to see how it goes on base 2... ;)
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
I agree with Brent. Take all arrangements of 3-digit numbers(1000 arrangements). All digits are equally represented. Remove any leading zeroes ('0' or '00') from the list. Remove '000' from the list. We have fewer zeroes now but all other numbers are equally represented. Adding '1000' at the end will not make up the deficit. So fewer zeroes but 1 has the greatest score because of '1000' David
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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.
Interesting one . . It's about two things - the Interval of integers under consideration and the fact that poor zero never gets to be the first (most significant) digit. For a range of 1 to 10^n, lucky "1" gets representation in both the first AND last, so has a count of one more than all the rest other than zero. Zero never starts an integer, so looses out greatly but does indeed benefit slightly from (n-1) representations in the last number in the series. I don't think I have ever actually replied to anything on CP - many thanks for interesting me so much as to prompt me to do so this time! Russ
A few are great. I am small. Together we are the Universe.
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In the range of 1-99 there are 20 1s alone!!!
Skipper: We'll fix it. Alex: Fix it? How you gonna fix this? Skipper: Grit, spit and a whole lotta duct tape.
Not in binary ;-)
