Problems of the Week - March 15 to March 20

Rewards for Problems of the week:

5 points for the correct answer at your level; 10 points for the next level; 20 points each for 2+ levels up.

 Lower Elementary:

Question: Sofia Kovalevskaya was born in Russia in 1850. When she was 17, she traveled 2,500 kilometers from Moscow to Heidelberg, Germany, because girls were not allowed to study math in Russia at the time. When she was 33, she moved another 1,750 kilometers to Stockholm, Sweden, to teach math at a university. How many kilometers did Sofia travel to get from Moscow to Heidelberg to Stockholm?

Upper Elementary:

Question: Hypatia was a Greek mathematician, philosopher, astronomer, and lecturer. In the morning, she gave 2–hour lectures about mathematics. Midday, she lectured about philosophy for 2 hours and 45 minutes. In the afternoon, she gave hour–and–a–half lectures about astronomy. In the evening, she again lectured about mathematics for 2 hours and 50 minutes. How much time did Hypatia spend lecturing each day?

 Middle School:

Question: Hedy Lamarr was born in 1914. She was a mathematician and inventor—without her, there would be no Wi-Fi or Bluetooth technology! She was also a famous actress. Her first film was released in 1930.  Twenty-nine more films and 26 years later, her final film was released. What was the average number of films Hedy Lamarr released each calendar year during her film–making career? (Give your answer as a fraction in lowest terms.)

 Algebra and Up:

Question: Most of us remember Florence Nightingale for her service as a wartime nurse, but did you know she was also an influential statistician? Her mathematical analysis of health conditions in India resulted in a decrease in mortality among soldiers of an average 12.5% each year. At the beginning of her campaign, there were 69 mortalities per 1,000 soldiers. What was the mortality rate at the end of her 10–year campaign? (Round to the nearest whole number per 1,000.)

Challenge problem to take home. 20 points for the correct answer. 

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It is possible to write the number 2021 as a difference of two squares:

2021 = 1011² - 1010².

Is there any other way to write 2021 as a difference of two squares?

Note: We are looking for a difference of squares of positive integers. Squares of negative numbers and non-integers don't count!