# High school contest

You are invited to participate in a math contest sponsored by the UH Manoa Math Department.

### The next contest will be held at:

• The University of Hawai’i at Mānoa
• Keller Hall 303
• December 15th, 2012, at 10am – 3:30pm
Lunch will be provided. The competition is open to all high school students in Hawai’i. Students may enter individually or as members of a school team. No registration is required for individual students.
Prof. Pavel Guerzhoy pavel@math.hawaii.edu
Department of Mathematics
University of Hawai`i
Honolulu, 96822
The mathematics is not part of the school curriculum. Contestants will have to draw on their logic and creativity to win.

### Sample Problem 1:

There is a path that a knight can take to go over a chessboard visiting each square exactly once. (It’s difficult to find, but not relevant to the problem.) Now remove the upper-right and lower-left squares. Is it still possible for the knight to go over each square exactly once?

Solution

### Sample Problem 2:

480 bugs are sitting on the squares of a 16×30 board, one bug in every square. We say that two bugs are neighbors if their squares share a side. They take off, and land on a 15×32 board, again one bug in every square. Is it possible that all former neighbors stay neighbors on the new board?

Solution

Contact Professor Guerzhoy for additional practice problems.

Contest Rules

The contest will consist of two sessions. The first session is from 10am until noon. The second session starts at 1pm. There is a lunch break in between. During each session the students will be offered a set of five problems, the same problems for each contestant. Each solution will be graded out of 10 points. Likely scores are 0,1, or 2 points in case of no or little progress towards a solution and 10, 9, or 8 for perfect or nearly perfect solutions. There is an emphasis on well-written solutions. Participants will work individually. The highest possible, but highly unlikely, score is 100. We suggest that students try to do well on a few problems that seem solvable to them. The contestant with the highest score wins. For the team competition we will add the scores of the three highest scoring team members. We will announce the results and winners publicly on the first math league meeting in Spring 2013.

#### Awards for individual achievements

• 1st Place: $100.00 • 2nd-4th Place:$50.00 (each)
• The best teams will also be recognized