Numbers Contest NUM3
This is my third Numbers Contest, NUM3
Reply ONLY by e-mail to momo@physics.ucsb.edu.
Do NOT post answers to any newsgroup.
Entries must reach here by Wednesday, July 11th, 12:12 P.M.
(L.A. time, zone -7).
I encourage everyone to enter my other contest, Common Entries MOJO3.
Note that the questions are virtually identical to questions asked in the
previous numbers contests, NUM1 and NUM2. There are only minor wording
differences. Results from NUM1 and NUM2 are included at the end of this post,
and will probably useful in determining your answers.
This is actually four COMPLETELY SEPARATE contests. You may choose to
skip some of the contests. However, please send your submissions for all the
contests that you choose to enter in a single e-mail -- do not send your
entries for separate contests in separate e-mails.
Here are the rules for determining the first place winners. Rules
for determining the second and third place winners for each contest
are described afterwards.
A: Pick a positive integer.
The first place winner will be the person who submits the smallest
positive integer that no one else submits. In the event that no
submitted number is unique (i.e. every person's entry is duplicated
by at least one other person), the first place position will be
declared vacant.
B: Pick three positive integers.
This is the same as contest A, except that you are allowed to submit
three positive integers (in a single e-mail, please), and the three
numbers that you submit will be treated as if they came from separate
individuals who happen to have the same name.
C: Pick an integer.
The first place winner will be the person who submits the smallest
unique integer which is greater than or equal to the median of all
integers submitted. In other words, if a single person submits the
median integer, he or she will win. But if multiple people submit the
median integer (or no one submits it), the winner will be the next highest
unique entry. In the event that there is no unique integer greater than
or equal to the median, the first place position will be declared vacant.
D: Pick three integers.
This is the same as contest C, except that you are allowed to submit
three integers (in a single e-mail, please), and the three numbers that
you submit will be treated as if they came from separate individuals who
happen to have the same name.
For each of the contests, the second place winners will be those
contestants who did not win first place, but could have won if a single
entered integer were removed. Similarly, the third place winners are those
who could have won if two entered integers were removed (and who did not win
first or second place). There are no fourth place winners. Note that in each
of the four contests, it is possible to have ties for second and third place,
and it is possible for any of the first, second, and third place positions
to be vacant. In contests B and D, because all three entered numbers are
treated separately, it is possible for a single person to win mutliple
positions in a single contest.
ALL INTEGERS SHOULD BE WRITTEN AS A SEQUENCE OF SIMPLE BASE TEN DIGITS.
There should be no algebraic manipulations, exponentials, or mathematical
definitions. Also, if a number is greater than 10^9, you should make
a note telling me how many digits are in it. Entries which do not satisfy
these conditions, or which do not fall into the ranges specified in each
contest, will be discarded.
For my convenience please do not quote this message when reponding.
You message should contain your answers, labeled A to D, and your name.
Additional comments, explanatory notes, explanations of strategy,
and suggestions for questions for future contests are all welcome, but
please place them after your five answers, and make sure that they are
clearly marked so as not to be confused with your answers. Your e-mail
address will be posted in the results if I don't see both a first and
a last name, or an explicit request for a particular form of your name
to be used.
Multiple entries are not allowed. Please do not post any discussion
of the questions to any newsgroup while the contest is in progress,
or collaborate with other contestants in your entries.
If you have questions about the rules, please e-mail me rather than
posting questions to the newsgroup. Results to parts of NUM1 and NUM2
appear below.
Have fun!
Momo Jeng (momo@physics.ucsb.edu)
----------------------------------------------------------------------
Results of NUM1 and NUM2
These questions were asked in previous Numbers Contests. There were
some minor wording differences.
A in NUM1 (27 entries)
2,3,3,4,4,5,5,5,5,5,6,6,6,8,8,9,9,9,10,10,11,11,11,12,12,13,23
Winner: 2 (Andrew Krywaniuk)
2nd: 13 3rd: 3,3,4,4,8,8,10,10,12,12,23
A in NUM2 (23 entries)
1,1,1,1,1,1,1,3,3,4,4,5,5,6,7,7,10,10,11,20,23,23,42
Winner: 6 (Nick Wedd)
2nd: 3,3,4,4,5,5,11 3rd: 7,7,10,10,20
B in NUM1 (78 entries)
1,1,1,1,1,1,2,3,3,3,3,4,4,5,5,5,5,5,6,6,7,7,7,7,8,8,8,8,9,
10,10,10,11,12,12,12,13,13,14,14,14,15,15,16,16,17,17,18,18,19,19,19,
20,20,20,22,22,22,22,22,23,23,23,24,24,24,25,26,26,28,
30,31,35,42,61,98,687,2751
Winner: 2 (Maree Cassidy)
2nd: 9 3rd: 4,4,6,6,11
B in NUM2 (69 entries)
1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,4,4,5,5,5,5,5,
6,6,7,7,7,7,8,8,8,9,10,10,11,11,12,12,13,14,15,15,19,23,23,23,24,24,24,25,
27,29,33,87
Winner: 9 (Mark Brader)
2nd: 4,4,6,6,13 3rd: 8,8,8,10,10,11,11,12,12,14
C in NUM1 (27 entries)
-6234584,-5,-5,-2,3,3,3,4,4,4,5,5,5,5,6,7,11,12,12,17,20,21,22,37,45,100,410
Winner: 6 (Tim Vaughan) (median=5)
2nd: 7 3rd: 11
C in NUM2 (23 entries)
-1,1,3,5,5,5,5,5,7,7,7,8,8,8,9,10,11,14,15,17,100,10000,9.99e99999
Winner: 9 (Michael Crowder) (median=8)
2nd: 10 3rd: 8,8,8,11
D was not asked in NUM1
D in NUM2 (67 entries)
-42,-3,0,1,2,2,2,3,4,4,5,5,5,6,6,6,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,
9,9,10,10,11,11,11,12,14,15,15,16,16,16,17,17,17,18,18,19,19,19,20,23,
41,42,43,100,200,300,1000,1000000,1000000
Winner: 12 (Keith Redo) (median=8)
2nd: 9,9,10,10,14 3rd: 11,11,11,20