Year: 2025

Solution to Mathematical Toy Box – AQ2024 #2

Prof. Bockting Problems & Solutions

The integers 1 thru 100 are written on individual cards, and those 100 cards are mixed into a hat. Aisha draws one card at a time, without replacement, until she draws a card relatively prime to all the cards she has already collected. What is the maximum number of cards Aisha could draw in this game?

Solution: 90.  One can construct a sequence of maximal length as follows:

  • Starting with 2, include all the even numbers from 2 through 100, a total of 50.
  • Ignoring 1, now include all the odd numbers that are not primes over 50. Since there are 10 primes between 50 and 100, there are 49-10=39 of these.
  • The 90th pick will now either be a 1 or a prime over 50, all of which will be relatively prime to all those on the list.

MAT Community Tea & Coffee Hour Dates for Winter 2025

Prof. Bockting Events

Throughout the year, the MAT Department hosts a number of informal events meant to help build and sustain our mathematical sciences community here at DePaul. These events provide an opportunity to meet with fellow MAT students, at both undergraduate and graduate levels, as well as MAT faculty members in a relaxed setting.

We will have five teas during the winter quarter:

  • Friday, 1/17 at 1:30-2:45 pm
  • Friday, 1/31 at 1:30-2:45 pm
  • Friday, 2/14 at 1:30-2:45 pm
  • Friday, 2/28 at 10:30-11:45 am (note the different time)
  • Friday, 3/14 at 1:15-1:55 pm (note the different time)

These community hours will take place in the MAT Department office suite (on the 5th floor of SAC, roughly SAC 546). Light refreshments, such as coffee, tea, and cookies, will be served. We hope that you can join us.