Numbers Contest NUM2
This is my second numbers contest, NUM2
Reply ONLY by e-mail to momo@physics.ucsb.edu.
Do NOT post answers to any newsgroup.
Entries must reach here by Monday, June 25th, 6 P.M. (L.A. time, zone -7).
I encourage everyone to enter my other contest, Common Entries MOJO2.
Note that four of the questions are virtually identical to questions
asked in the first numbers contest, NUM1, which was ran several weeks
ago. There are only some minor wording differences. Results from
NUM1 are included at the end of this posting.
This is actually five 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.
E: Pick an integer.
The first place winners will be those who pick the second largest integer
of those in the contest. Ties are possible. That is, it is possible that
multiple people will pick the highest integer, and/or multiple people will
pick the second highest integer -- in that event, all those picking the
second highest integer will tie for first place. If everyone picks
the same integer, the first place position will be declared vacant.
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 five 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 E, 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 appear
below, and may be useful if you are unclear on the rules.
Have fun!
Momo Jeng (momo@physics.ucsb.edu)
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Results of NUM1
Questions A, B, C, and E of the above contest were asked in NUM1. Question D
is new. There are some wording differences in the rules, but IN MY OPINION,
none of the changes are significant enough to bother resposting the rules to
NUM1 here. You are encouraged to check the old posting of "Numbers Contest NUM1"
on google groups if you think wording could be significant.
A (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
1st:2 2nd:13 3rd:3,3,4,4,8,8,10,10,12,12,23
B (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
1st:2 2nd:9 3rd:4,4,6,6,11
C (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
1st:6 2nd:7 3rd:11
E (22 non-disqualified entries) (4 entries were disqualified)
Note : The rules prohibit entrants from using scientific notation,
but I use it here to save space. However, I truncate numbers
rather than rounding them.
5,7,4.2e1,3.53e2,4.41e2,9.78e2,1.21e3,1.00e5,1.07e7,9.99e8,9.99e9,
9.99e16,9.99e18,6.84e21,5.55e24,9.99e29,8.81e43,1.00e68,9.99e99,
9.99e167,3.21e319,1.23e999998
1st: 3.21e319 2nd:9.99e167 3rd:9.99e99
Note : The 1st, 2nd, and 3rd place entries are completely written
out in my posting of "NUM1 results"