Results to Numbers Contest NUM3
Not so many entrants this time! Only 11, one of whom declined to
enter contests A and C (and who was probably not serious about B
and D, either). I mentioned in the results to NUM2 that this would
probably be my last Numbers Contest, and the low number of entrants to
this one confirms my prior decision (unless I come up with new,
interesting questions). My feeling is that the contest was less interesting
to enter when repeated, but that it made the results more interesting (to
me, at least).
Contest A
First Place : 2 John McLeod
Second Place : 3 Eric Beaumont
Third Place : 1 Michael Crowder
1 Paul Guertin
1 Stephen Perry
9 James Morse
Contest B
First Place : 1 Paul Bolchover
Second Place : 3 Eric Beaumont
Third Place : 2 Andrew Krywaniuk
2 John McLeod
5 Boolbar
Contest C
median=11
First Place : 11 Gerrit de Blaauw
Second Place : 13 John McLeod
Third Place : 15 Paul Guertin
Contest D
median=15
First Place : 18 Eric Beaumont
Second Place : 17 Michael Crowder
17 Gerrit de Blauuw
21 Andrew Krywaniuk
Third Place : 16 Gerrit de Blauuw
16 John McLeod
16 Michael Crowder
23 Paul Bolchover
Prizes for everyone! With 22 awards (1st, 2nd and 3rd) and 11 entrants,
there was plenty for everyone! As usual, since the four contests are
completely separate, there is no way of determining an "overall" winner.
But assuming that all four contests are valued the same, and that
the values of the awards go 1st>2nd>3rd, there are two entrants
whose total award value is greater than anyone elses, and not clearly
comparable to each other.
Eric Beaumont : 1st, 2nd, 2nd
John McLeod : 1st, 2nd, 3rd, 3rd
-----------------------------------------------------------------------------
Below I reproduce the rules for determining the first place winner,
and the list of all numbers entered, and also make some comments.
>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.
First, let's recall the results from NUM1 and NUM2:
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
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
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
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
And here are the rather slim results from NUM3:
Contest A (10 entries) (NUM3) :
1,1,1,2,3,4,4,7,7,9
Contest B (33 entries) (NUM3):
1,2,2,3,4,4,4,5,6,6,6,7,7,8,8,8,9,9,10,11,11,13,14,16,17,18,21,27,28,29,
999,999999,9999999
On B I had thought, after the first two contests, that "1" would never
be a good choice, since there would always be a few people willing to
use up one of their three choices on "1". Apparently I wasn't the
only one to reason that way. Of course, had there been more entrants,
"1" might have turned out to be not as good. One of the defects of this
contest (at least, I consider it a defect), is that figuring out a good
choice depends on making a good estimate of the number of entrants.
>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.
Again, we first recall the results from prior contests:
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
median=5
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
median=8
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
median=8
And now for the results of this contest:
Contest C (10 entries) (NUM3) :
7,7,10,10,10,11,13,14,14,15
median=11
Contest D (33 entries) (NUM3) :
7,7,8,8,9,9,10,11,12,13,13,13,14,14,14,14,15,15,15,15,16,16,16,17,17,
18,19,19,21,23,55555,555555,5555555
median=15
In NUM1 the median was 5, and in NUM2 the median was 8 for both
contests C and D. I made comments in the results to NUM2 that it
seemed pretter obvious that the median should get larger each contest.
So I expected almost everyone to give answers greater than 8 this
time. As you can see, the median did in fact grow. I would be curious to
see how fast the median would grow if this contest was repeated a
bunch of times, and to look at the acceleration, rate of change of
the acceleration, etc. . . I think this could be interesting, since
if the median grew by 3 each new contest (for example), once people
anticipated this, they should pick answers more than 3 greater,
accelerating the increase of the median. But, of course, since I'm
not planning a NUM4 (and it doesn't seem like there would be much
interest anyway), we'll never know. Perhaps someone has a different
idea for a similar sort of contest?
Anyway, that's it. As I said, there won't be a NUM4 unless I think of
exciting new questions. And I'm going to be travelling for the next
3-5 weeks, so it will be a while until MOJO4 as well.
Thanks to everyone who entered!
Momo
------------------------------------------------------------------------
Here are the entries with names. NE means "not entered".
To fit everything into the columns, I make the following abbreviations:
X=999, XX=999999, XXX=9999999
Y=55555, YY=555555, YYY=5555555
A B C D
AndrewKrywaniuk 4 2 4 6 14 13 19 21
Boolbar 7 5 7 9 10 9 11 13
Divya Mittal NE X XX XXX NE Y YY YYY
Eric Beaumont 3 3 13 28 10 10 15 18
Gerrit deBlaauw 4 4 10 11 11 14 16 17
James Morse 9 16 17 18 14 12 13 14
John McLeod 2 2 4 6 13 14 15 16
Michael Crowder 1 6 7 8 10 15 16 17
Paul Bolchover 7 1 8 14 7 7 15 23
Paul Guertin 1 8 9 11 15 8 14 19
Stephen Perry 1 21 27 29 7 7 8 9