Vandal Science News - October 2017
I have been serving as Dean of the College of Science for just over two months, but I am already beginning to feel at home both professionally and personally. The University of Idaho offers a welcoming environment for the entire community, and that is something of which we are rightly proud. As one example, I was able to participate in some of the activities for new students and parents at the beginning of the new academic year, and I was impressed by the way the university strives to help all students find their place in the campus community. What a supportive learning environment for our students!
There is much going on this fall in the college. Our 13th annual Student Research Exposition will highlight the work of many of our student researchers, both graduate and undergraduate. Providing our students with opportunities to engage in the work of scientific research remains a point of distinction for us. It’s exciting to see what they achieve with those opportunities. We are pleased to note that the college has increased undergraduate enrollment again this fall, which is not surprising given the strong job market for students majoring in science and mathematical disciplines.
Our faculty members continue to excel as well. The College of Science saw another record-breaking year in external funding, and several breakthroughs by Idaho researchers were given national attention. I hope you will enjoy reading about some of the highlights here in this issue of the Vandal Science News. As always, thank you for your support of the College of Science.
– Dean Ginger E. Carney
Glacier Park’s Forest Health is Subject of Research
A College of Science mapping research project is examining damage caused by insects in Glacier National Park.
2017 College & Department Award Winners
The College of Science and Departmental Awards for the Class of 2017.
Vandal Science News Puzzler
With each issue of the Vandal Science News we'll include a challenging puzzle. Send solutions by email to firstname.lastname@example.org – we'll post the names of those who submit correct solutions in the next issue.
Puzzler for October 2017
Our puzzler for this issue uses some arithmetic, but mostly logic. Have fun!
A company runs two locations in the same town. Between the two they employ 225 workers.
- One week, exactly 1/5 of the workforce at one location is transferred across town to the other location.
- Then, the next week, exactly 1/4 of the then-present workers at one location are transferred to the other location.
- Finally, the week after that, exactly 1/3 of the workers then stationed at the Westside location are transferred to the Eastside location.
- After this last transfer, the difference between the two workforces is 21 workers.
How many workers were originally employed at the Westside location?
The Westside factory started with 105 workers.
We'll get to that answer by using a little algebra and a little reasoning about divisibility. To begin with, let's call our two factories A and B and suppose that A is the one making the first transfer. Then to begin with, A has 5x workers and B has 225-5x workers. The first transfer is to move x workers from A to B, so the effect is:
Before: A has 5x, B has 225-5x
After: A has 4x, B has 225-4x
Now the number 225-4x is not divisible by 4, so factory B can't make the second transfer! So, the second transfer must consist of moving another x workers (one-fourth of A's current total) from A to B:
Before: A has 4x, B has 225-4x
After: A has 3x, B has 225-3x = 3(75-x)
Now there are two cases to consider.
CASE 1: If the third transfer also goes from A to B then it also amounts to moving x workers from A to B:
Before: A has 3x, B has 225-3x
After: A has 2x, B has 225-2x
Then, the difference between the two must be 21, so:
2x - (225-2x) = 21 or 2x - (225-2x) = -21
This means that 4x is either 246 or 204. The first of these is not a multiple of 4, so it must be that 4x = 204. This gives us x = 51. The only problem with this is that factory A started with 5x workers, and 5x would be greater than 225. So, Case 1 has led us to a dead end!
CASE 2: We are left with the conclusion that the last transfer was from B to A. (Note that this means that factory B is the Westside factory -- we know the last transfer went from west to east.) This transfer must have consisted of moving 75-x workers (one-third of B's current workforce) from B to A:
After: A has 3x, B has 3(75-x)
Before: A has 3x+(75-x) = 75+2x, B has 2(75-x) = 150-2x
The difference between the two must be 21, so:
(75+2x) - (150-2x) = 21 or (75+2x) - (150-2x) = -21
This means that 4x is either 96 or 54. But 54 is not a multiple of 4, so it must be that 4x = 96, or x = 24.
The Westside factory, as we mentioned, is factory B. So, it started with 225-5x = 225-5*(24) = 105 workers.
- Christopher Birkinbine (Physics, 2013)
- Chris Marx (UI Biological Sciences Department)
- Greg Stenback (Geological Engineering, 1985; MS Statistics, 1987)
- Alex Wezensky(Mathematics and Computer Science, 2018)
- Brenna Wong (Chemical Engineering, 2015)