Math Club Meeting Announcement
1:30 p.m. Thursday September 29th in Pegasus Room, SU 2.502 (behind the Pub)
Short talk: Euler, the Mozart of Mathematics, by Dr. Paul Stanford
The Electrician's Problem, student solutions and the author's solution
Discussion of Dr. Andreescu's "Good Number" problem
Discussion of the Putnam handout material (full Putnam meeting will be the following week)
And of course, FREE PIZZA
Meeting ends 3:30. We expect to meet every Thursday this semester except Thanksgiving.
Congratulations
To our new club officers:
President Jennifer Wollscheid (nice to have another President Jennifer!)
Vice President Omar A Shankles
Secretary Sam Blair
Treasurer Lacy Bishline
And welcome to new club members.
Euler, the Mozart of Mathematics
The Basil Problem and other feats of daring virtuosity
Dr. Stanford will give a reasonably short talk on this amazing mathematician, whose collected works are still being published!
Puzzles
The Electrician's puzzle is available at
http://www.utdallas.edu/~phs031000/mathclub/puzzle/electrician.html.
Record during the meeting, that you may wish to beat, were as follows. Notation (u,v) means that the group found a solution for u wires that involved only v trips. These are not necessarily the best possible - you could do better!
(0,0) (1,0) (3,2) (4,3) (5,4) (6,2) (7,3) (8,4) (9,3) (10,2)
I can announce that the 5 wire record has been beaten: a student supplied a clever 3-trip solution.
Come on Thursday to show what you can do, and finally to be given the solution (unless the vote says to wait another week!).
Good Numbers
Dr. Andreescu's problem of the week, drawn from a USA mathematical Olympiad, is as follows:
A natural number n is called "good" if it is the sum a1+a2+a3+...+ak of positive integers that have the property that the sum of their reciprocals 1/a1 + 1/a2 + ... + 1/ak = 1.
For example, 11 is good because 11 = 2 + 3 + 6, and 1/2 + 1/3 + 1/6 = 1.
If a number isn't good, it's bad. Some bad numbers are 2, 3, 5, 6, 7 -- which you can see by trying all the possibilities.
Part (a) of the puzzle is: If it is given that 33, 34, 35, ... , 73 are all good numbers, show that all bigger numbers are good.
part (b) is to find all good numbers, without making any such assumption.
[This is a paraphrase of the original problem -- I trust it is essentially correct.]
Dr. Andreescu gave some further hints at the last meeting, one of which was that if your know n is good, then 2n+2 must also be good. (Why?) Also, 9, 10 and 11 are good.
A much harder variation is to characterize all the Very Good numbers. This is the same puzzle as above, but the numbers a1, a2, etc must all be different! (So it is related to Egyptian fractions.) The answer is not known to the proposer even!
Pizza
And if nothing else excites you, come for the free pizza (donations gratefully accepted), and good company.
Regards,
Dr. Paul Stanford
Friend and Former Advisor to the Math Club
for
Dr. Titu Andreescu
Mathclub Advisor
Jennifer Wollscheid
Mathclub President