|
Search: id:A102508
|
|
|
| A102508 |
|
Round table problem: Suppose you have a round table with, at regular distances, chairs around it. The chairs form a regular polygon. n persons are seated on n of these chairs. The other chairs are unoccupied. a(n) is the maximum number of chairs so that, if a waiter puts two glasses (randomly) on the table, in front of two (different) chairs, it is always possible to turn the table so that the two glasses end up in front of two chairs with two persons on it. |
|
+0
2
|
| |
|
|
OFFSET
|
2,1
|
|
|
COMMENT
|
It is easy to show that a(n) cannot be more than n(n-1)+1.
This problem is a circular analogue of an optimal ruler problem; see A004137. - David Wasserman (dwasserm(AT)earthlink.net), Apr 15 2008
Solutions do not always exist for table sizes less than a(n). For example, for n = 5 there is no solution for a table of size 20. - David Wasserman (dwasserm(AT)earthlink.net), Apr 15 2008
95 <= a(11) < 109. - David Wasserman (dwasserm(AT)earthlink.net), Apr 15 2008
a(12) = 133. - David Wasserman (dwasserm(AT)earthlink.net), Apr 15 2008
|
|
EXAMPLE
|
a(5)=21 because if we have 21 chairs, 5 persons can sit down on chairs 1, 4, 5, 10 and 12. 1=5-4 (mod 21). 2=12-10 (mod 21). 3=4-1 (mod 21). 4=5-1 (mod 21). 5=10-5 (mod 21). 6=10-4 (mod 21). 7=12-5 (mod 21). 8=12-4 (mod 21). 9=10-1 (mod 21). 10=1-12 (mod 21). It is impossible to do the same with 22 or more chairs.
|
|
CROSSREFS
|
Cf. A004137.
Sequence in context: A073896 A077853 A025721 this_sequence A115298 A161206 A025728
Adjacent sequences: A102505 A102506 A102507 this_sequence A102509 A102510 A102511
|
|
KEYWORD
|
more,nonn
|
|
AUTHOR
|
Ard Van Moer (ard.van.moer(AT)vub.ac.be), Mar 15 2005
|
|
EXTENSIONS
|
3 more terms from David Wasserman (dwasserm(AT)earthlink.net), Apr 15 2008
|
|
|
Search completed in 0.002 seconds
|
