# Tag Archives: mystery

## A Genetics Riddle

Along with his brothers, a soldier goes off to war leaving behind his wife and two sons. Six years later he returns to his family after losing both his brothers in action. Something is different though. His wife suspects something, but can’t put her finger on it. She just knows that something is different about her husband. Over the next two years, the family grows by twins (a boy and a girl) and then another girl. Then, in an auto accident, the husband dies and his widow decides that she can now investigate a hunch she has had for some time without upsetting her husband.

That month, she takes all of her children in for their annual checkup and vaccines, and also asks the doctor to check her blood type along with all of the children.

The results, mailed to her (see below) later that week, give her a start as she realizes her hunch was correct.

What was her hunch? How did she arrive at her conclusion?

Posted by on March 27, 2016 in Uncategorized

Tags: , , , , ,

## Cryptography

Today is the first day of the Coursera Cyrptography class taught by Stanford Professor, Dan Boneh. I follow courses like this every once in a while in order to learn a bit about topics that I would not otherwise get any exposure to. Boneh’s course is a little math-intense, but there is another more concept-driven course on the same topic being offered on Khan Academy. If you haven’t taken advantage of either of these two sites, you should look into them. Both are entirely free, and both are taught by excellent educators.

Here’s a video from the Khan Academy site introducing the Caesar Cipher, a simple cipher like those used on radio dramas of the past (get your secret decoder ring!).

If you want to crack a simple substitution cipher like this, you might want to start by using a frequency chart of letters used in the English language, like this one:

The Caesar cipher: Brit explains the Caesar cipher, the first popular substitution cipher, and shows how it was broken with “frequency analysis”

However, once you figure out the easiest letters (e,t,and a), things get a bit more difficult. At this point, you will probably have to start looking at letter pairings (Bigrams) to see if any useful patterns show up there. Here’s a listing of the most common Bigrams (again, in English).

It’s interesting that these kinds of codes might ever have been considered sophisticated enough to use in the real world. After all, it’s easy to find examples of these types of ciphers in daily newspapers around the world presented as cryptograms that people do for fun.

KT RPP EXRDJ PXZ’J KX BOXD EVDIXI,

KSZ DBZ JB BOXD EVDIXI ZQRZ BSA KARVDJ YRPP BSZ.

-AVWQRAI IRCNVDJ

Posted by on September 8, 2014 in Education

## A blood typing mystery

A positive blood typing example, thanks to biologycorner.com for the figure

A commenter raised the following as an example of a highly unusual blood type pattern within a family.

Given:

Parent #1 (female) Blood type O- (i/i,Rh-/Rh-)

Parent #2 (male) Blood type AB+ (IA/IB, Rh+/?)

Child #1 O- (i/i,Rh-/Rh-)

Child #2 Blood type AB+ (IA/IB, Rh+/?)

Is this possible?

Indeed, this is a highly questionable situation. Given that the genetics of ABO typing are fairly well described, the situation described raises a lot of flags. Assuming what is presented is an honest case, it would be extraordinarily interesting to investigate.

If I were asked to solve this, I would probably pursue the following ideas…

Before doing anything else, I would have everyone in the family re-typed. Since questions have been raised, I would insist that they were all re-typed at least three times at three facilities (or at least using different lots of the test reagents). I would also question the original typing location about the reagents used in the initial test and pursue whether any additional questionable typings were reported. Additionally, records should indicate the lots used for the original typing. I would question the company that produced these reagents about Quality Assurance and any known problems with these lots.

The commenter also indicated that he knew of several couples with this situation (which would be extraordinary). Again, this is unlikely, so the local testing facility  and its quality remain likely sources of error.

Luckily, an explanation for the Rh types of both child is possible. Assuming the father is Rh+/Rh-, and the mother is Rh-/Rh-, children could easily have either type. This is a relief, because the Rhesus gene has a large number of alleles making it more complex genetically.

Regarding ABO types, the simplest explanation for Child #1 is that it is not the father’s child. This leaves the ABO type of child#2 in question. Assuming the retyping tests suggested above come back completely supporting the original characterization, I would like to see the birth records for the child to verify that it was not adopted or even somehow ‘switched at birth’. The best verification would be an RFLP analysis of both parents and the child. This is the ‘DNA Fingerprinting’ that is talked about in the courtroom.

Probably the most interesting explanation is that the mother is a chimera. This rare condition arises when an individual starts out life as two non-identical twins that fuse early in development to become a single person. Confirming this would require a battery of RFLP tests from different locations of the body.

To be honest, I suspect this example to be apocryphal. But it provides a great example for describing how science is done. It is always important to remember that the tests we are talking about are just tools and subject to all the weaknesses of any other human pursuit. If we found fingerprints at a crime scene, we could feel quite confident that the owner of those prints was present at some time, but we don’t know with certainty that that person is actually guilty. Thank you very much for providing the topic!