Results to Numbers Contest NUM2
Here are the results for Numbers Contest NUM2. There were 23 entrants.
I found the results pretty interesting, so. . .
I have just posted Numbers Contest NUM3, which simply repeats questions
A through D of this contest. I thus ask that you NOT discuss the results
of this contests, since the questions are identical. Judging from NUM1,
there's not a lot to discuss anyway. (Unless you find a mistake in the
scoring, in which case I hope you will e-mail me first.)
I encourage everyone to enter NUM3! It will probably be the last Numbers
Contest (at least in the near future).
Here are the winners to NUM2.
Contest A
First Place : 6 Nick Wedd
Second Place : 3 Andrew Krywaniuk
3 Paul Guertin
4 Andy Jakcsy
4 Mike Shreeve
5 Mark Brader
5 Papik Meli
11 Monsieur Bottineau
Third Place : 7 Boolbar
7 Jeromy Labit
10 Eric Jensen
10 Gerrit de Blaauw
20 Andrew Bolt
Contest B
First Place : 9 Mark Brader
Second Place : 4 James Morse
4 Patrick Hamlyn
6 Andrew Bolt
6 Boolbar
13 Monsieur Bottineau
Third Place : 8 Boolbar
8 Mark Brader
8 Mike Shreeve
10 Eric Jensen
10 Gerrit de Blaauw
11 Andrew Krywaniuk
11 Keith Redo
12 Andrew Krywaniuk
12 Keith Redo
14 Paul Guertin
Contest C
median=8
First Place : 9 Michael Crowder
Second Place : 10 Gerrit de Blaauw
Third Place : 8 Andrew Bolt
8 Eric Jensen
8 Nick Wedd
11 Andrew Krywaniuk
Contest D
median=8
First Place : 12 Keith Redo
Second Place : 9 Michael Crowder
9 Nick Wedd
10 Eric Jensen
10 Rick Zepp
14 Gerrit de Blaauw
Third Place : 11 Keith Redo
11 Michael Crowder
11 Mike Shreeve
20 Mark Brader
I did not allow the use of scientific notation, but I use it in posting
the results to contest E, since these numbers are quite large. However, I
truncate the numbers, rather than rounding them.
Contest E
First Place : 9.99e18499 Gerrit de Blaauw
Second Place : 9.00e15000 Andrew Krywaniuk
Third Place : 9.99e999 Mike Shreeve
Because the nature of the rules encourages many-way ties, 48 awards (1st,
2nd, and 3rd place) were given out in these five contests. So the average
position was won by three people, and the average contestant won two positions.
However, the rules prevented any first place position from being a tie.
These were five completely separate contests, so there is no way of
determining an "overall" winner. But it is worth mentioning that some
contestants did quite well in multiple contests, and Gerrit de Blauuw
seems to have the best case for declaring himself the overall winner.
Here are the contestants who either won four or five contests, or three
contests including a 1st place position:
Andrew Krywaniuk (2nd, 2nd, 3rd, 3rd, 3rd)
Eric Jensen (2nd, 3rd, 3rd, 3rd)
Gerrit de Blaauw (1st, 2nd, 2nd, 3rd, 3rd)
Mark Brader (1st, 2nd, 3rd, 3rd)
Michael Crowder (1st, 2nd, 3rd)
Mike Shreeve (2nd, 3rd, 3rd, 3rd)
Nick Wedd (1st, 2nd, 3rd)
Keith Redo (1st, 3rd, 3rd,3rd)
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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:
Contest A (27 entries) (NUM1):
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
Contest B (78 entries) (NUM1):
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
The "obvious" choice of 1 garnered no votes in A, but was the most common
answer in B. Apparently people were not willing to "waste" their sole vote
on such an obvious choice, but were willing to give up one of their three
choices on it. Interestingly, the result was that 2 won in both contests.
Does this make 2 the obvious choice? Well,. . .
Contest A (23 entries) (NUM2):
1,1,1,1,1,1,1,3,3,4,4,5,5,6,7,7,10,10,11,20,23,23,42
Contest B (69 entries) (NUM2):
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
Now no one was willing to "waste" their sole vote on 2, which won both
contests last time. So no one picked 2 in contest A, but it was the most
common choice in contest B! Seven of the twenty-three entrants (30%) picked
1 in contest A. 1 and 3 tied for the second most common in contest B. I
found this rather neat.
>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.
Contest C (23 entries) (NUM2)
-1,1,3,5,5,5,5,5,7,7,7,8,8,8,9,10,11,14,15,17,100,10000,9.99e99999
In NUM1 the median was 5, and the winner was 6. Given that the rules
give an upward push to entries, I thought that it was obvious that the
median this time would be greater than 5. I also thought that this would
be obvious to almost everyone, and that thus all entries would be greater
than 5, and thus that the median would be significantly greater than 5.
As you can see, I was wrong. The new median was 8, and the winner was 9.
I would have guessed that the median would go up to 13 or so.
>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.
Contest D (67 entries) (NUM2)
-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
Here I again thought that almost all entries would be greater than 5. Also,
with three times as many entries, and the requirement of uniqueness, I thought
that the entries would be even higher than in contest C, and that the
median in D would be larger than that in C. But the median was 8 in both.
So I again predicted wrongly.
>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.
Scientific notation was NOT allowed, but to save space, I (sort of)
use it here. However, numbers are truncated, rather than rounded (9997
becomes 9.99e3, not 1.00e3).
Contest E (19 entries) (NUM2)
1,1,5,7,256,318,666,5.93e13,4.45e14,8.88e43,5e260,1e299,3.21e318,3.21e319,
7.77e776,9.99e999,9e15000,9.99e18499,4.24e41999
One entrant skipped contest E. Three of the answers to this question were
disqualified by the following rules:
>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.
3 disqualified entries:
999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999991
9.99e501
The first two are greater than 10^9, and did not tell me how many digits were
in the numbers, while the third was in scientific notation. I should
probably mention that Msr. Bottineau's disqualified entry of 9.99e501 was
entered in response to my correction post, which did not repeat all the
rules -- so my typo error may have been unfair to him, in that he would
perhaps have noticed the above rule if he had been responding to the original
post. But none of these three entries would have affected the winners of
this contest anyway.
As many people pointed out, there was a typo when I first posted this. I wrote
"second smallest integer" in the first line instead of "second largest
integer." I invited everyone who was thus misled into sending a small number
to resubmit. At least two of the small numbers (1 and 7) were
intentional (joke answers). Andrew Bolt's answer of 1 came with strategy
notes, which I think are interesting enough to repeat here:
>My strategy for E is to assume that everyone else will realise that the
>second biggest number will still be huge, and that they could
>theoretically generate a huge e-mail containing a viably big entry,
>but can't be bothered. As a result, I predict that only one other
>person will submit a number for this category.
>
>Actually, the above is fairly unlikely, but the coolness factor of
>winning the contest with the number '1' makes it the ideal answer.
>
>Andrew
I am not repeating contest E in NUM3, partially because I think it's a
little too random to make any good guesses on, and partially because I'm
tired of getting 20,000 or 1,000,000 digit numbers.
In case you forgot, here are the rules for determining second and third
place winners for all five contests:
>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. There are no fourth
>place winners. . .
Well, that's it. Again, I hope that everyone will enter the currently posted,
and final Numbers Contest, NUM3, which simply repeats questions A-D of
this contest, and refrain from commenting on NUM1 and NUM2, or responding to
my comments here, until the conclusion of NUM3.
Thanks to everyone who entered!
Momo
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Here are the entries with names.
NE means "not entered". DQ means "disqualified". Scientific notation
was NOT allowed, but to save space, it is (sort of) used in answers to E,
with "5.55 24" indicating 5.55*10^24. However, numbers are truncated,
rather than rounded (9996 becomes 9.99e3, not 1.00e3).
To fit everything into the columns, I make the following abbreviations:
XX=9.99e99999 YY=1000 ZZ=1000000
A B C D E
Andrew Bolt 20 6 15 24 8 41 42 43 1 0
AndrewKrywaniuk 3 3 11 12 11 17 18 19 9.00 15000
Andy Jakcsy 4 3 15 29 -1 -3 2 6 5.93 13
Boolbar 7 6 7 8 7 6 7 8 5.00 260
Dave Gates 1 1 2 3 7 6 7 8 1 0
David Hill 23 1 23 87 XX 2 NE NE NE
Eric Jensen 10 10 24 27 8 4 7 10 4.24 41999
Gerrit deBlaauw 10 1 5 10 10 14 16 17 9.99 18499
Herve Bourgeois 23 23 24 25 1 1 2 3 3.21 318
James Morse 1 2 3 4 3 4 6 8 1.00 299
Jeromy Labit 7 2 7 23 7 6 7 8 7.77 776
John Gerson 1 1 2 3 15 15 16 17 3.18 2
Kev Stone 42 1 2 3 100 100 200 300 6.66 2
Keith Redo 1 11 12 19 5 11 12 19 2.56 2
Mark Brader 5 7 8 9 14 16 18 20 8.88 43
Michael Crowder 1 1 2 33 9 7 9 11 DQ
Mike Shreeve 4 2 5 8 5 5 8 11 9.99 999
Msr. Bottineau 11 1 5 13 17 15 19 23 DQ
Nick Wedd 6 1 3 5 8 7 8 9 3.21 319
Patrick Hamlyn 1 2 3 4 5 6 7 8 DQ
Papik Meli 5 1 2 5 10000 YY ZZ ZZ 5 0
Paul Guertin 3 2 7 14 5 0 5 -42 4.45 14
Rick Zepp 1 1 2 3 5 5 8 10 7 0