Gus Wirth wrote:
> I looked at the programming contest description for this event 
> <http://icpc.baylor.edu/icpc/> this year and realized that there is an 
> error in their problem description. Their first problem states that a 
> couple with A+ and B+ blood types can have a child with any blood type. 
> This is false if both parents have both alleles the same for either type 
> (AA or BB) or the Rh factor (++). I hope the students noticed this error.

Given the information, I would have to agree that the problem as stated
is correct. The information that we have is blood type A+ and B+. There
are numerous combinations that it can be brought about:
AA++    BB++
AA+-    BB+-
AO++    BO++
AO+-    BO+-

We simply don't know which one (from each column) to pick. Therefore, we
must conclude that it is possible for a couple with A+ and B+ blood
types to produce a child with any of the eight blood types, if the
parents have AO+- and BO+- combinations.

If we knew more about the lineage, we may be able to rule out potential
combinations (if the mother's parents were both AB+, then the mother is
either AA++ or AA+- combination, so we can rule out her child having O+,
O-, B+ or B- blood types), and thus rule out certain blood types (such
as the Os, or Rh -s). With enough information, we might also be able to
determine that any child of that couple would be AB+.

I tried to keep my terminology consistent.

-john

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