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Category: Permutation and Combination

I-have-6-friends-and-during-a-vacation-I-met-them-during-several-dinners-I-found-that-I-dined-with-all-the-6-exactly-on-1-day-with-every-5-of-them-on-2-days-with-every-4-of-them-on-3-days-with-eve

Question Number 21686 by Tinkutara last updated on 30/Sep/17 Ihave6friendsandduringavacationImetthemduringseveraldinners.IfoundthatIdinedwithallthe6exactlyon1day;withevery5ofthemon2days;withevery4ofthemon3days;withevery3ofthemon4days;withevery2ofthemon5days.Furthereveryfriend$$\mathrm{was}\:\mathrm{present}\:\mathrm{at}\:\mathrm{7}\:\mathrm{dinners}\:\mathrm{and}\:\mathrm{every} \

In-a-group-of-ten-persons-each-person-is-asked-to-write-the-sum-of-the-ages-of-all-the-other-9-persons-If-all-the-ten-sums-form-the-9-element-set-82-83-84-85-87-90-91-92-find-the-individual

Question Number 21685 by Tinkutara last updated on 30/Sep/17 Inagroupoftenpersons,eachpersonisaskedtowritethesumoftheagesofalltheother9persons.Ifallthetensumsformthe9elementset{82,83,84,85,87,90,91,92}findtheindividualagesofthepersons(assumingthemtobewholenumbersofyears). Terms…

Suppose-A-1-A-2-A-20-is-a-20-sided-regular-polygon-How-many-non-isosceles-scalene-triangles-can-be-formed-whose-vertices-are-among-the-vertices-of-the-polygon-but-whose-sides-are-not-the-side

Question Number 21683 by Tinkutara last updated on 30/Sep/17 SupposeA1A2A20isa20sidedregularpolygon.Howmanynonisosceles(scalene)trianglescanbeformedwhoseverticesareamongtheverticesofthepolygonbutwhosesidesarenotthesidesofthepolygon?