Quandaries
and Queries 

Math Problem: Sally went to a farm to buy eggs. Returning home, she gave half of them to her sister who, in turn, gave a third of those she had gotten to her boyfriend. The latter, after eating one third of the eggs that he had gotten, gave the rest to his cousin. Given that each egg weighs 70 grams, that Sally cannot carry more than 2.5kg, and that the eggs were raw, calculate how many eggs the cousin of Sally's sister's boyfriend received. Michael 

Hi Michael, What has the condition "the eggs were raw" to do with the problem? I think it's to tell you that you can't cut an egg in half. Every person must get an integer number of eggs. Sally gave half of her eggs to her sister. Can you finish the problem now? Michael replied "If I see it right the answer is 2 eggs". Hi again Michael,Suppose that Sally has 2 eggs. She gives half of her eggs to her sister, so she gives one egg to her sister. Her sister then "gave a third of those she had gotten to her boyfriend". She can't do this because the eggs are raw and she can't split one egg into thirds. To give a third of her eggs to her boy friend, Sally's sister must have at least 3 eggs. If Sally's sister has 3 eggs then Sally must have started with 6 eggs, so lets start again. Suppose that Sally has 6 eggs. She gives half of her eggs to her sister, so she gives 3 eggs to her sister. Sally's sister has 3 eggs and gives one third of her eggs to her boy friend. Thus she gives 1 egg to her boy friend. Her boy friend eats one third of the eggs he was given. Again he can't do this because he can't divide the one eggs he has into thirds. So, what is the smallest number of eggs he could have? In this case how many eggs did sally start with? Penny 

