K9 Logic Answers

Question

For those of you not familiar, a rebus uses pictures to represent words or parts of words.  In this case the rebus below represents a 3-letter word.  Good luck, and as they say, a picture is worth a thousand words, or in this case a single 3-letter word.

Answer

We've taken some liberties in interpreting the pictograms to make it a bit
tougher for all you well-educated readers. We'll go line by line:
"pole" + "im" + "er" + "ace" = polymerase
"ch" + "ain" = chain (anyone at a more advanced age may easily recognize
joint pain when they see it)
"re" + "act" + "shun" = reaction (all images of Indiana Jones we're copy
righted, so we did our best)

So the correct answer is PCR.

Question

 Dr. Orange began her lecture on the structure of the cytoskeleton with a quick review of geometry - just to get her students' minds warmed up.

"All right students, I've handed out six toothpicks to each of you." Dr. Orange continues, "Now create a shape in which there are only four corners by using all six toothpicks."

The students were quickly smiling as they started to assemble various shapes, until Dr. Orange added,

"One more thing. Every time the toothpicks meet the angle created needs to be less than 180 degrees, and the toothpicks cannot cross-over each other."

Describe a shape which meets the criteria set forth by Dr. Orange.

Answer

Like Captain James Kirk in the iconic Wrath of Khan, you need to think in three dimensions to get this puzzle correct. The answer is the 4 sided tetrahedron or pyramid. A remarkably simple form, the tetrahedron is useful in many mechanical engineering solutions – including scaffolding of the cytoskeleton.

Question

“Oh! This interdisciplinary conference I organized was a complete failure” laments Dr. Green.

“That is too bad, what went wrong?” Dr. Orange sympathetically replies.

“Well, it all started when the four scientific luminaries I invited, a string-theory physicist, a molecular ecologist, a geo-biologist and genetics ethicist, just had no idea what the others worked upon.” Green continues “Dr. A. Aye kept querying Dr. G. Ravitas about geothermal bacterial growth, and Dr. T. Phyllis kept referring to Dr. Ugine as a tree hugging ecologist.  Ravitus thought Aye was the genetics ethicist, and Ugine was convinced that Phyllis was into string theory.  And similarly with the rest of them; each of the four misidentified the other three, though no two made the same misidentification. Finally, Dr. A. Aye stormed out of the room screaming I am going back to my research in Lemure species diversity.”

Now, knowing that Dr. Aye was the molecular ecologist, can you correctly deduce the area of research for Dr. Phyllis?

Answer

Dr. Phyllis is the Geo-Biologist.
The key to solving this problem is to organize the data correctly.  First create the chart below from what can derived from the puzzle:

The key is to realize that no row or column will contain the same profession.  Thus, using deductive logic, initially each square has two possible choices except for the Aye’s column which each have only one choice each.  The next step completes the solution for Aye’s real and assumed professions:

Using the same logic, and knowing that no one will guess their own profession as someone else’s profession, the rest is easily deduced as follows – much like a Sudoku:

Question

This time we join Dr. Orange in the midst of a conversation with the undergraduate students in her fly genetics lab. She is trying to hammer home some simple concepts regarding fly genetics, and decides that a little mathematics problem is the best way to get their neurons firing. Dr. Orange says "Class, here is a lab culture vial containing seventeen flies with one of four non-lethal eye phenotypes: white eyes, orange eyes, red eyes, and eyeless" as she shows them the vial. "Whoever can count the number of flies with wild-type red eyes will earn extra credit today." She proceeds to allow each student thirty seconds to try and count the wild-type flies. Soon after they start, the students complain it is just too hard to count the peppy flies. She then proffers up the final bits of information necessary to solve the problem, "Oh, and by the way, flies with red eyes are the most abundant. Neither of the four phenotypes have the same number in the vial. There are at least two of each color. And if I randomly pick enough flies, and only just enough flies, from the culture to ensure that I have at least two of any one eye type and one of any second phenotype, I must pick 11 flies." Can you answer Dr. Orange's question about the number of wild-type red eyes correctly and earn a bobble head?

Answer

The answer is 7 flies have wild-type red eyes. With the information provided there are only three possible distributions:

         1)  8      4      3      2
         2)  7      5      3      2
         3)  6      5      4      2

The trick is the by choosing 11 you are guaranteed to have at least 1 red eye fly. This eliminates 8 red eyes, as the minimum number of flies to guarantee one red eye is 10, and it likewise eliminates 6 red eyes as the number is 12. So that mutant eye types from the middle set add up to 10 (5+3+2=10) + 1 red eye = 11.

Question

We are invited back to Dr. Green's lab in which he is giving a lecture on translation and transcription.  To drive home a point Dr. Green points out "digits are only symbols, we could use symbols instead. Suppose that S E is the square of E.  Then S N E N might also represent another square."

"I don't see that, Dr. Green" points out Ness, not one of Dr. Green's more gifted students. 

"Why doesn't it surprise me, NESS, that you don't SEE it?  Well just stop and think about it, hmm ....." Dr. Green further muses "this gives me an idea."  Dr. Green proceeds to write on the white board:

                                    S E E

                              + N E S S

                                  _ _ _ _

"Which of you can correctly sum these two numbers now that I have already given values to N E and S?" Green challenges the lab mates. "And please provide the answer in my notation." 

Answer

The answer is NNNN. This is a simple sum. S E must be either 25 or 36. A little testing will show that it can’t be 25, for there isn’t a perfect square of 2 x 5 x. So S E must be 36, and then that makes S N E N equal to 3969 which is 632. Thus N is 9. So back to the question: the sum of S E E and N E S S is the sum of 366 and 9633, or 9999. In Dr. Green’s notation is equal to NNNN.