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I found Bob's story very hard to believe, so I just dealt
myself a poker hand and got the 2 of spades, the 7 of hearts,
the 8 of spades, the Jack of clubs and the Jack of hearts.
I'm sure you can imagine my surprise! I calculate the odds
of getting that hand to be only one in nearly 2.6 million!
Sorry for doubting you, Bob!
John Mallinckrodt
Cal Poly Pomona
On Feb 18, 2014, at 8:01 AM, LaMontagne, Bob wrote:
I was playing poker last night and was dealt a hand thatwas 5-6-7-8-9 all hearts. Was that random - or did the dealer
fix the hand?
two lists with so few numbers.
There is no test that can truly tell the randomness of the
Of Rauber,
Bob at PC
-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf
probabilistic guess.Joel
Sent: Tuesday, February 18, 2014 10:47 AM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution ( math challenge)
The second list was the random list. As noted, one cannot prove
which one was the random list, you can only make a
numbers in
I looked at two factors, the number of times consecutive numbers
appear -> leads to 2nd list is random The number of times
ranges, whichthe range [30-35] appeared compared to the other decade
me that thealso lends evidence that the second list was the random one.
I didn't personally calculate it, but the Math Prof. told
random listprobability of consecutive numbers appearing on a truly
Of Jeffreyis 48%, much higher than most people would guess.
-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf
Philip KellerSchnick
Sent: Monday, February 17, 2014 8:49 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution ( math challenge)
Only two of the numbers in the first list end in 0. Thus, I think
the first list was made up by people.
________________________________________
From: Phys-l [phys-l-bounces@phys-l.org] on behalf of
feel the[pkeller@holmdelschools.org]
Sent: Monday, February 17, 2014 6:59 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution ( math challenge)
I am going the other way here. I think the students would
that in 21need to choose a wide range of numbers. But I calculate
to have nosets like this, we would expect just under 5 of the sets
batch as student-generated.single-digit numbers. The first batch has 2 like that, and the
second has 6. So I pick the second batch as real, 1st
take a simple
On 2/17/2014 4:04 PM, Donald Polvani wrote:
Not being familiar with random number tests, I had to
been arranged(and
crude) test. If the numbers are truly random and have
expected the havein numerical order, then the first column would be
numbers between 8numbers from 1 - 7, with successive columns having
column limits- 14, 15 - 21,
22 - 28, and 29 - 35.
So a very simple test is to simply count the number of times that
numbers in each column exceed (or fall below) the expected column
limits. For the first set of numbers, I find that the
the lastwere exceeded, respectively, 5, 8, 6, 4, and 5 times (for
of numberscolumn I counted the number of times the listed number fell below
the lower column limit). Doing this for the second set
for the lastproduced the excess numbers 8, 11, 10, 4, and 7 (again,
tests morecolumn I counted the number of times the listed number fell belowlower column limit).
the
Clearly the second set of numbers failed the column limit
Of Rauber,often and should be (i.e. "probably is") the student list.
Don
Dr. Donald Polvani
Anne Arundel Community College
Adjunct Faculty, Physics (Retired)
Arnold, MD
--Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf
smallest toJoel
Sent: Monday, February 17, 2014 2:08 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution ( math challenge)
Before giving it away, both lists are in numerical order
generated.largest; so that has been ordered after the numbers were
Of Jeffrey
-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf
group wasSchnick
Sent: Monday, February 17, 2014 11:32 AM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution ( math challenge)
Each set of five numbers in the first set is listed in numerical
order from smallest to largest. Thus, I think the first
Behalf Of Paulstudentgenerated.
-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On
uniformlyNord
Sent: Monday, February 17, 2014 12:28 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my
institution ( math challenge)
That's easy.
The first group is the real lottery numbers. It is more
that hasdistributed.
In the second set, the student-generated numbers, numbers in the
20's are much preferred.
Paul
On Feb 17, 2014, at 10:33 AM, Rauber, Joel
<Joel.Rauber@SDSTATE.EDU>
wrote:
The below may be tangentially related to discussions of entropy35. This is the same as the "South Dakota Cash Lottery"
(See subject heading)
I asked my Math 316 (Discrete Math) to randomly pick 5 numbers
from
1 to
They weredrawings twice a week. I told them that I would compare their
"random" numbers to actual numbers drawn in the lottery.
responses,instructed to try to make their numbers as random as possible so
they looked just like the real random numbers. I had 21
2014. Canthey are in one of the two lists below. The other list is the
numbers drawn in the lottery from Dec 7, 2013 to Feb 15,
is an easy,you tell which list is the student's list? Hint: there
_______________________________________________almost trivial,way to do this, or least to locate the most likely student list.
______________________________________________________________________________________________
02-06-07-25-34
03-09-12-15-34
06-16-21-28-32
06-10-13-21-23
04-18-26-27-34
03-06-17-27-32
03-11-21-22-35
01-02-08-17-27
07-12-14-24-31
03-07-14-18-27
07-13-22-25-31
07-12-23-31-32
04-17-18-22-35
08-15-17-20-25
12-16-18-29-34
02-07-11-16-21
08-23-24-32-35
17-19-23-29-31
09-16-27-28-32
06-15-19-26-32
06-13-15-23-31
11-17-19-28-31
03-11-29-32-35
14-21-24-28-33
09-14-22-23-31
03-21-26-30-31
05-15-20-27-29
02-23-24-25-26
07-13-20-24-25
03-23-26-27-28
06-20-21-26-29
01-10-14-19-35
12-18-27-32-35
02-06-24-27-28
03-08-11-21-30
09-14-20-25-31
04-13-19-21-28
10-11-12-21-31
02-07-11-20-24
06-17-25-29-30
13-23-24-26-34
09-17-21-25-26
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