Results to Numbers Contest NUM1
Here are the results for Numbers Contest NUM1. There were only 27 entrants.
One entered only contests A and C, while the rest entered all five
contests. I had hoped for more entrants, since this contest doesn't take
long to enter. However, perhaps some people were put off by the fact that
it was almost impossible to make really good reasoned guesses to C and E.
Hopefully if I do another numbers contest, I will get more entrants,
since people will have a better idea about "acceptable" ranges. Or
perhaps I should just stick to Common Entries Contest. . .
Here are the winners:
Contest A
First Place : 2 Andrew Krywaniuk
Second Place : 13 Maree Cassidy
Third Place : 3 James Morse
3 Jacob Stone
4 Josh
4 Tim Vaughan
8 Paul Atkinson
8 Duncan Booth
10 Gerrit de Blaauw
10 Eric S. Jensen
12 Michael Davidson
12 Rhodent
23 herve.bourgeois@laposte.net
Contest B
First Place : 2 Maree Cassidy
Second Place : 9 Andrew Krywaniuk
Third Place : 4 Patrick Hamlyn
4 Jacob Stone
6 Patrick Hamlyn
6 Jacob Stone
11 Andrew Hartley
(The repeated names are not typos -- see the original rules posting)
Contest C
First Place : 6 Tim Vaughan
Second Place : 7 Jacob Stone
Third Place : 11 Heidi King
Contest D
First Place : 3 Mark Brader
3 Brian Coombs
3 Stephen Merriman
3 James Morse
3 Jacob Stone
Second Place : VACANT
Third Place : VACANT
Contest E
First Place : 32153215321532153213542135432133213543013215321532
15321532135421354321332135430132153215321532153213
54213543213321354301321532153215321532135421354321
33213543013215321532153215321354213543213321354301
32153215321532153213542135432133213543013215321532
15321532135421354321332135430132153215321532153213
54213543213321354301 (320 digits) Darryl Tam
Second Place: 99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
999999999999999999 (168 digits) Gerrit de Blaauw
Third Place : 99999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999
(100 digits) Andrew Krywaniuk
These were five completely separate contests, so there is no way of
determining an "overall" winner. But it is worth mentioning that three
contestants did quite well in multiple contests: Andrew Krywaniuk (1st,
2nd, and 3rd), Maree Cassidy (1st, 2nd, and 3rd), and Jacob Stone (1st,
2nd, 3rd, 3rd, and 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: Submit 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.
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
This question was the main reason that I ran this contest. It was
inspired by Mark Brader's last Rare Entries Contest, MSB19, in which
he asked for a word beginning with the letters "fuc", and in which
no contestant answered the obvious obscenity. It inspired an argument
over whether 1 would be a good answer for this question.
I think these results are pretty cool. All the small integers appear
except 1 and 7, which were the most common answers when "pick a number"
was asked in my recent Common Entries Contest, MOJO1. Furthermore, every
other number in the range 3-12 is repeated. The winner was 2, and if anyone
had picked 1, that would have won. If anyone had picked 7, they would have
gotten 2nd place.
A ridiculous number of entrants tied for 3rd place.
>B: Submit three positive integers.
> This is the same as contest A, 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.
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
The idea here was basically the same as the last one, but to see what
happened when there were three times as many entries. Surprisingly, the
winner was again 2.
The first and second place winner's names were the same here as in contest A,
although their order was reversed.
>C: Submit an integer (positive or negative).
> 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.
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
As one entrant pointed out, there was a problem with the wording to this
question. The parenthetical comment, "(positive or negative)" was meant
to simply clarify that any integer was OK, but inadvertently ruled out 0.
I decided that a second post clarifying that 0 was OK would cause more
problems than it would solve, by calling special attention to the number 0.
I hope that this error in phrasing didn't significantly affect anyone's
strategy.
Unlike in contests A, B, and D, I don't think it was really posssible here
to reason out a best answer. I certainly didn't have any strong feelings
for what would be the best choice. I was, however, surprised by the number
of negative numbers and small single-digit numbers. In contest A the
condition of smallness pushed the numbers down, and the condition of
uniqueness pushed them up. Here all the conditions tend to push the numbers
up, so I expected only positive integers, and for most of them to be
double-digit numbers.
>D: Pick a positive integer.
> The first place winners will be those who pick the second smallest
> integer of those in the contest. Here ties are possible. For example,
> if there are 10 contestants, and 2 pick u, 3 pick v, 4 pick w, and 1
> picks x, where x>w>v>u, then the three people who picked v will tie for
> first place (u, v, w, and x, are, of course, positive integers).
> If everyone picks the same integer, the first place position will be
> declared vacant. Note that while you may pick 1, it is impossible
> for 1 to win.
26 entries:
2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,4,7,7,7,10,12,18,24,84,100000
I don't know why I included the third sentence in the instructions.
I doubt that it made the question clearer for anyone.
This question was more interesting in theory, than in practice. I hope most
people saw the logical chain that ruled out picking any number, under the
same logic as the "Unexpected Hanging" problem. Here, 1 cannot possibly win,
so no will pick 1. Everyone knows this, so we might as well not consider 1
to be a possible choice, which makes 2 the lowest possible number. So 2 cannot
possibly win, and no one will pick 2. We repeat this argument and use
induction to rule out all numbers. So no integer can win! But, of course,
some integer must actually win. I was curious to see how low people would
be willing to go.
I didn't realize that people would go as low as 2, but in retrospect, the
analysis seems clear. As one entrant who picked 2 commented, he expected
that at least one "smart-ass" would pick 1. While it wasn't clear that
he was correct (he wasn't), his argument was certainly reasonable, and, in
retrospect, it's clear that at least one entrant would make that argument.
So it should have been clear that the winner would either be 2 or 3 (although
I didn't anticipate this).
>E: Pick an integer
> This is similar to contest D, but here the first place winners will be
> those who pick the second largest integer of those in the contest.
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).
22 non-disqualified entries:
5,7,42,353,441,978,1210,1e5,1.07e7,9.99e8,9.99e9,9.99e16,9.99e18,
6.84e21,5.55e24,9.99e29,8.81e43,1.00e68,9.99e99,9.99e167,3.21e319,
1.23e999998
That last, largest number, is not a typo. The entrant sent in a 20,000
line e-mail! He expressed hope that someone else would send in a million-digit
number. As you can see, that was by far the largest number submitted.
Four 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.
4 disqualified entries:
5689654548547 (greater than 10^9, without a note on the number of digits)
10^100 (use of exponential)
googol (not written as a sequence of digits)
3 folowed by a million zeros (not written as a sequence of digits)
If these numbers had been allowed, they would have changed the winner,
because the last answer, "3 followed by a million zeros," would have
been the new largest number. Of course, it's not clear what I mean by
this contrafactual, since if I had allowed such numbers, other entrants
would surely have given similarly large numbers, and if the last entrant
had realized that these sorts of answers were disallowed, he probably
wouldn't have gone to the trouble of actually writing out a million
zeros. If the answers of "googol" and "10^100" had been written out (and
the "3 followed by a million zeros" had not), they would have tied for
third place.
I hope it's clear why I required that the numbers actually be written
out, and to be told the number of digits. Question E creates a sort of
"arms race" for producing large numbers. Without any restrictions, I
might have gotten large numbers that were difficult to compare to one
another (like 9^(9^(9^9)) and (6^66)!), or even worse, people might have
created their own notation (like the Knuth up-arrows) to create large numbers
which would not be expressable with standard mathematical symbols in a
e-mail-sized file. Some of you may remember the results to Douglas
Hofstadter's "Luring Lottery."
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. . .
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Here are the entries with names, in the order that they were received.
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).
A B C D E
Patrick Hamlyn 5 4 5 6 5 2 5.55 24
Russ Perry Jr. 6 1 17 31 12 18 1.07 7
Jon Persky 11 22 22 23 22 2 DQ
Mark Brader 9 14 18 19 4 3 8.81 43
Brian Coombs 6 14 15 16 4 3 6.84 21
Heidi King 5 NE 11 NE NE
Michael Shreeve 11 3 7 17 21 4 9.99 29
James Morse 3 1 3 5 3 3 DQ
Gerrit deBlaauw 10 20 22 24 20 2 9.99 167
Andrew Hartley 9 10 11 12 4 4 1.00 68
Tim Vaughan 4 22 23 24 6 12 9.99 18
AndrewKrywaniuk 2 1 8 9 -5 2 9.99 99
Papik Meli 5 5 7 20 3 4 5 0
herve.bourgeois 23 24 25 26 12 24 3.53 2
@laposte.net
Eric S. Jensen 10 5 10 42 -5 10 4.2 1
MichaelDavidson 12 12 23 35 5 2 1.23 999998
Darryl Tam 6 13 16 18 17 4 3.21 319
Maree Cassidy 13 2 7 13 3 100000 1.00 5
Jacob Stone 3 4 5 6 7 3 9.99 9
Josh 4 1 19 2751 -6234584 84 1.21 3
Rhodent 12 12 19 61 100 4 9.78 2
Paul Atkinson 8 1 8 14 -2 7 7 0
Duncan Booth 8 1 8 22 5 2 9.99 8
Paul Guertin 11 3 7 28 37 7 4.41 2
StephenMerriman 5 10 20 30 5 3 DQ
Kevin Stone 9 8 98 687 45 7 DQ
Daniel Unger 5 3 15 26 410 4 9.99 16