We encourage all math and stat majors to participate in the Problem of the Week competition for fun and possibly prizes. There are two divisions (undergrad and grad). The top 3 finishers in each division are eligible for prizes. Check out https://sites.google.com/a/sjsu.edu/bjackson/home/sjsuproblemoftheweek for more info. The first problem is given below and solutions are due by Sept. 3. Hard copies of problems and solutions can be found in the hallway outside of the math office MH 308 or you can also check online on Professor Jackson’s google site linked above.
Problem 1 (5 points)
Let m be a positive integer and consider the number N = m(m + 2015). Find a positive integer m such that N is a perfect square.
Aug. 27 – Sept. 9, 2015
Problem 2 (6 points)
In the Math Department raffle each ticket has a 6-digit decimal number (000000-999999). A raffle ticket is said to be “lucky” if the sum of the first 3 digits is equal to the sum of the last 3 digits. Show that the sum of the numbers on all of the lucky raffle tickets is divisible by the “unlucky” number 13.
Solutions to Problem #2 should be submitted to the math office MH 308 or Professor Jackson’s office MH 316 or online to bradley.jackson@sjsu.edu by Wednesday Sept. 9 at 12:00 pm
Sept. 3 – Sept. 16, 2015
Problem 3 (7 points) Two players, Alex and Brad, take turns removing marbles from a jar which initially contains 2015 marbles. Assume that on each turn the number of marbles withdrawn is a power of two. If Alex has the first turn and the player who takes the last marble wins, is there a winning strategy for either of the players?
Solutions to Problem #3 should be submitted to the math office MH 308 or Professor Jackson’s office MH 316 or online to bradley.jackson@sjsu.edu by Wednesday Sept. 16 at 12:00 pm
Cheers, Brad J