Pigeonhole Principle in combinatorics [duplicate]












-1















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  • Combinatorics - pigeonhole principle question

    1 answer




A field worker has to make altogether 43 visits, at least one on each day. Is there a period of consecutive days on which he makes exactly 21 visits if he makes his visits on 22 days? What happens to the problem if he makes his visits on 23 days instead of 22 days?



How can I approach to solve this problem using Pigeonhole principle, thanks.






combinatorics







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marked as duplicate by Carl Mummert, Cesareo, max_zorn, Chinnapparaj R, choco_addicted Nov 29 at 7:42


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.















  • Variations of this question have been asked and answered on this website many times. I'll see if I can find them.... math.stackexchange.com/questions/97397/… and math.stackexchange.com/questions/571937/… and math.stackexchange.com/questions/1145254/… and math.stackexchange.com/questions/1271126/…
    – Gerry Myerson
    Nov 26 at 11:48












  • Also math.stackexchange.com/questions/1636571/… and math.stackexchange.com/questions/1853532/… and math.stackexchange.com/questions/2163546/… and math.stackexchange.com/questions/2413861/… and math.stackexchange.com/questions/2512137/… and many more.
    – Gerry Myerson
    Nov 26 at 11:52












  • Are you sure that your figures are right, because I'm trying to solve it and the result is not coming as expected.
    – Sauhard Sharma
    Nov 26 at 12:00










  • Actually, the given figures are right and I didn't find similar questions that enable me to solve the problem and that is why I post it here, thank you.
    – 2468
    Nov 26 at 12:55
















-1















This question already has an answer here:




  • Combinatorics - pigeonhole principle question

    1 answer




A field worker has to make altogether 43 visits, at least one on each day. Is there a period of consecutive days on which he makes exactly 21 visits if he makes his visits on 22 days? What happens to the problem if he makes his visits on 23 days instead of 22 days?



How can I approach to solve this problem using Pigeonhole principle, thanks.






combinatorics







share|cite|improve this question















marked as duplicate by Carl Mummert, Cesareo, max_zorn, Chinnapparaj R, choco_addicted Nov 29 at 7:42


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.















  • Variations of this question have been asked and answered on this website many times. I'll see if I can find them.... math.stackexchange.com/questions/97397/… and math.stackexchange.com/questions/571937/… and math.stackexchange.com/questions/1145254/… and math.stackexchange.com/questions/1271126/…
    – Gerry Myerson
    Nov 26 at 11:48












  • Also math.stackexchange.com/questions/1636571/… and math.stackexchange.com/questions/1853532/… and math.stackexchange.com/questions/2163546/… and math.stackexchange.com/questions/2413861/… and math.stackexchange.com/questions/2512137/… and many more.
    – Gerry Myerson
    Nov 26 at 11:52












  • Are you sure that your figures are right, because I'm trying to solve it and the result is not coming as expected.
    – Sauhard Sharma
    Nov 26 at 12:00










  • Actually, the given figures are right and I didn't find similar questions that enable me to solve the problem and that is why I post it here, thank you.
    – 2468
    Nov 26 at 12:55














-1












-1








-1








This question already has an answer here:




  • Combinatorics - pigeonhole principle question

    1 answer




A field worker has to make altogether 43 visits, at least one on each day. Is there a period of consecutive days on which he makes exactly 21 visits if he makes his visits on 22 days? What happens to the problem if he makes his visits on 23 days instead of 22 days?



How can I approach to solve this problem using Pigeonhole principle, thanks.






combinatorics







share|cite|improve this question
















This question already has an answer here:




  • Combinatorics - pigeonhole principle question

    1 answer




A field worker has to make altogether 43 visits, at least one on each day. Is there a period of consecutive days on which he makes exactly 21 visits if he makes his visits on 22 days? What happens to the problem if he makes his visits on 23 days instead of 22 days?



How can I approach to solve this problem using Pigeonhole principle, thanks.





This question already has an answer here:




  • Combinatorics - pigeonhole principle question

    1 answer







combinatorics




combinatorics






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 26 at 11:33









Yanko

5,801723




5,801723










asked Nov 26 at 11:31









2468

505




505




marked as duplicate by Carl Mummert, Cesareo, max_zorn, Chinnapparaj R, choco_addicted Nov 29 at 7:42


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.






marked as duplicate by Carl Mummert, Cesareo, max_zorn, Chinnapparaj R, choco_addicted Nov 29 at 7:42


This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.














  • Variations of this question have been asked and answered on this website many times. I'll see if I can find them.... math.stackexchange.com/questions/97397/… and math.stackexchange.com/questions/571937/… and math.stackexchange.com/questions/1145254/… and math.stackexchange.com/questions/1271126/…
    – Gerry Myerson
    Nov 26 at 11:48












  • Also math.stackexchange.com/questions/1636571/… and math.stackexchange.com/questions/1853532/… and math.stackexchange.com/questions/2163546/… and math.stackexchange.com/questions/2413861/… and math.stackexchange.com/questions/2512137/… and many more.
    – Gerry Myerson
    Nov 26 at 11:52












  • Are you sure that your figures are right, because I'm trying to solve it and the result is not coming as expected.
    – Sauhard Sharma
    Nov 26 at 12:00










  • Actually, the given figures are right and I didn't find similar questions that enable me to solve the problem and that is why I post it here, thank you.
    – 2468
    Nov 26 at 12:55


















  • Variations of this question have been asked and answered on this website many times. I'll see if I can find them.... math.stackexchange.com/questions/97397/… and math.stackexchange.com/questions/571937/… and math.stackexchange.com/questions/1145254/… and math.stackexchange.com/questions/1271126/…
    – Gerry Myerson
    Nov 26 at 11:48












  • Also math.stackexchange.com/questions/1636571/… and math.stackexchange.com/questions/1853532/… and math.stackexchange.com/questions/2163546/… and math.stackexchange.com/questions/2413861/… and math.stackexchange.com/questions/2512137/… and many more.
    – Gerry Myerson
    Nov 26 at 11:52












  • Are you sure that your figures are right, because I'm trying to solve it and the result is not coming as expected.
    – Sauhard Sharma
    Nov 26 at 12:00










  • Actually, the given figures are right and I didn't find similar questions that enable me to solve the problem and that is why I post it here, thank you.
    – 2468
    Nov 26 at 12:55
















Variations of this question have been asked and answered on this website many times. I'll see if I can find them.... math.stackexchange.com/questions/97397/… and math.stackexchange.com/questions/571937/… and math.stackexchange.com/questions/1145254/… and math.stackexchange.com/questions/1271126/…
– Gerry Myerson
Nov 26 at 11:48






Variations of this question have been asked and answered on this website many times. I'll see if I can find them.... math.stackexchange.com/questions/97397/… and math.stackexchange.com/questions/571937/… and math.stackexchange.com/questions/1145254/… and math.stackexchange.com/questions/1271126/…
– Gerry Myerson
Nov 26 at 11:48














Also math.stackexchange.com/questions/1636571/… and math.stackexchange.com/questions/1853532/… and math.stackexchange.com/questions/2163546/… and math.stackexchange.com/questions/2413861/… and math.stackexchange.com/questions/2512137/… and many more.
– Gerry Myerson
Nov 26 at 11:52






Also math.stackexchange.com/questions/1636571/… and math.stackexchange.com/questions/1853532/… and math.stackexchange.com/questions/2163546/… and math.stackexchange.com/questions/2413861/… and math.stackexchange.com/questions/2512137/… and many more.
– Gerry Myerson
Nov 26 at 11:52














Are you sure that your figures are right, because I'm trying to solve it and the result is not coming as expected.
– Sauhard Sharma
Nov 26 at 12:00




Are you sure that your figures are right, because I'm trying to solve it and the result is not coming as expected.
– Sauhard Sharma
Nov 26 at 12:00












Actually, the given figures are right and I didn't find similar questions that enable me to solve the problem and that is why I post it here, thank you.
– 2468
Nov 26 at 12:55




Actually, the given figures are right and I didn't find similar questions that enable me to solve the problem and that is why I post it here, thank you.
– 2468
Nov 26 at 12:55










1 Answer
1






active

oldest

votes


















0














If he makes his visits on 22 days, there need not be a period of consecutive days on which he makes exactly 21 visits. He could make one visit each day for the first 20 days, then 22 visits on the 21st day, and one visit on the 22nd day. That's $20+22+1=43$ visits, at least one each day for 22 days, and clearly no set of consecutive days with exactly 21 visits.



For the 23-day version, I'd suggest having another look at the links I posted in the comments, as I am confident the methods used in those links will cover this case.






share|cite|improve this answer





















  • Any thoughts, 2468?
    – Gerry Myerson
    Nov 30 at 3:18


















1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









0














If he makes his visits on 22 days, there need not be a period of consecutive days on which he makes exactly 21 visits. He could make one visit each day for the first 20 days, then 22 visits on the 21st day, and one visit on the 22nd day. That's $20+22+1=43$ visits, at least one each day for 22 days, and clearly no set of consecutive days with exactly 21 visits.



For the 23-day version, I'd suggest having another look at the links I posted in the comments, as I am confident the methods used in those links will cover this case.






share|cite|improve this answer





















  • Any thoughts, 2468?
    – Gerry Myerson
    Nov 30 at 3:18
















0














If he makes his visits on 22 days, there need not be a period of consecutive days on which he makes exactly 21 visits. He could make one visit each day for the first 20 days, then 22 visits on the 21st day, and one visit on the 22nd day. That's $20+22+1=43$ visits, at least one each day for 22 days, and clearly no set of consecutive days with exactly 21 visits.



For the 23-day version, I'd suggest having another look at the links I posted in the comments, as I am confident the methods used in those links will cover this case.






share|cite|improve this answer





















  • Any thoughts, 2468?
    – Gerry Myerson
    Nov 30 at 3:18














0












0








0






If he makes his visits on 22 days, there need not be a period of consecutive days on which he makes exactly 21 visits. He could make one visit each day for the first 20 days, then 22 visits on the 21st day, and one visit on the 22nd day. That's $20+22+1=43$ visits, at least one each day for 22 days, and clearly no set of consecutive days with exactly 21 visits.



For the 23-day version, I'd suggest having another look at the links I posted in the comments, as I am confident the methods used in those links will cover this case.






share|cite|improve this answer












If he makes his visits on 22 days, there need not be a period of consecutive days on which he makes exactly 21 visits. He could make one visit each day for the first 20 days, then 22 visits on the 21st day, and one visit on the 22nd day. That's $20+22+1=43$ visits, at least one each day for 22 days, and clearly no set of consecutive days with exactly 21 visits.



For the 23-day version, I'd suggest having another look at the links I posted in the comments, as I am confident the methods used in those links will cover this case.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered Nov 29 at 0:19









Gerry Myerson

146k8147298




146k8147298












  • Any thoughts, 2468?
    – Gerry Myerson
    Nov 30 at 3:18


















  • Any thoughts, 2468?
    – Gerry Myerson
    Nov 30 at 3:18
















Any thoughts, 2468?
– Gerry Myerson
Nov 30 at 3:18




Any thoughts, 2468?
– Gerry Myerson
Nov 30 at 3:18



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