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Re: [Phys-L] From a Math Prof (physics BS major) at my institution ( math challenge)



Yup, there is an old Feynman story of similar ilk.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of John Mallinckrodt
Sent: Tuesday, February 18, 2014 10:10 AM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my institution ( math challenge)

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 that was 5-6-7-8-9 all hearts. Was that random - or did the dealer fix the hand?

There is no test that can truly tell the randomness of the two lists with so few numbers.

Bob at PC

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Rauber,
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 probabilistic guess.

I looked at two factors, the number of times consecutive numbers
appear -> leads to 2nd list is random The number of times numbers in
the range [30-35] appeared compared to the other decade ranges, which
also lends evidence that the second list was the random one.

I didn't personally calculate it, but the Math Prof. told me that the
probability of consecutive numbers appearing on a truly random list
is 48%, much higher than most people would guess.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Jeffrey
Schnick
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 Philip Keller
[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 feel the
need to choose a wide range of numbers. But I calculate that in 21
sets like this, we would expect just under 5 of the sets to have no
single-digit numbers. The first batch has 2 like that, and the
second has 6. So I pick the second batch as real, 1st batch as student-generated.


On 2/17/2014 4:04 PM, Donald Polvani wrote:
Not being familiar with random number tests, I had to take a simple
(and
crude) test. If the numbers are truly random and have been arranged
in numerical order, then the first column would be expected the have
numbers from 1 - 7, with successive columns having numbers between 8
- 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 column limits
were exceeded, respectively, 5, 8, 6, 4, and 5 times (for the last
column I counted the number of times the listed number fell below
the lower column limit). Doing this for the second set of numbers
produced the excess numbers 8, 11, 10, 4, and 7 (again, for the last
column I counted the number of times the listed number fell below
the
lower column limit).

Clearly the second set of numbers failed the column limit tests more
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 Of Rauber,
Joel
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 smallest to
largest; so that has been ordered after the numbers were generated.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Jeffrey
Schnick
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 group was
student
generated.

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Paul
Nord
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 uniformly
distributed.
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 entropy
(See subject heading)


I asked my Math 316 (Discrete Math) to randomly pick 5 numbers
from
1 to
35. This is the same as the "South Dakota Cash Lottery" that has
drawings twice a week. I told them that I would compare their
"random" numbers to actual numbers drawn in the lottery. They were
instructed to try to make their numbers as random as possible so
they looked just like the real random numbers. I had 21 responses,
they 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, 2014. Can
you tell which list is the student's list? Hint: there is an easy,
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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