Hi citizens! I've finally managed to collect problems of various difficulty for the first Whyville Mathematical Olympiad. This competition will hopefully be a yearly event, hosted in July, much like the real International Mathematical Olympiad. In fact, if you check, there should be a mathematical olympiad for whatever country you're in now.

Here's how the Whyville Olympiad (WMO) will work. Everyone is invited. You will be given 3 questions, each worth an equal 7 marks. The top scorers will receive medals and clam prizes, and the A+ medal will be awarded to citizens who have displayed even a small hint of inginuity. You will have one week from the day this article is posted to submit your solutions to my inbox (by Ymail) with the title "Whyville Mathematical Olympiad".

I will check all solutions and answers to all questions. There may be more than one answer in several cases. So without further delay, here is the first Whyville Mathematical Olympiad!

1. Anne leaves town A travelling by bike to town B along a certain path at sunrise. Bart leaves town B travelling by bike to town A along the same path as Anne. They travel at a constant speed, and do not stop biking towards their final destinations. The cross each other's paths at noon. Anne gets to town B at 5:00pm and Bart gets to town A at 11:15pm. At what time was sunrise? (7 points)

2. Show that there is no perfect square whose digits sum of to 2006. (7 points)

3. Two natural numbers, x and y, are taken such that their sum is less than 100. (x + y < 100) Both x and y are greater than 1. Sam is told the sum of the numbers (x + y) and Pam is told the product of the numbers (xy). Neither of them knows the original two numbers, x and y. They have the following conversation:

Pam: I cannot determine the sum of the numbers
Sam: I know.
Pam: Now, I know their sum.
Sam: Now, I know their product.

Determine x and y. (7 points)

Note: a natural number is a whole number greater than 0 . . . so that means any number like 1, 2, 3, 4, 5 . . . up to infinity!

21 points in total. Contestants are given one week from date of article.

Remember, if you even attempt a question, you will probably receive marks for it. First place winner will receive 10000 clams, second place scorer will receive 6000 clams and third place scorer will receive 4000 clams. Medals will be given to citizens who display any amount of inginuity in trying to solve a problem. All entries will be read. All marks will be posted in my city records once the competition is finished. I will then write an ariticle to display the results, the winners, the prizes, the solutions, and when you can expect the next Whyville Mathematical Olympiad.

P.S. Everyone can enter!! Even City workers! Citizens of all ages!

Thanks a lot everyone. Best of luck to all of you!
Deriko