A newsagent offered a paperboy a choice of how he would like to be paid. "I'll give you $1 today, $2 tomorrow, $3 the next day and so on for 2 weeks. Or, I will give you 1 cent today, 2 cents tomorrow, 4 cents the next day and I'll keep doubling for the fourteen days. Which offer would result in the most money after fourteen days and how much will this be?

A farmer is taking her eggs to market in her cart, but she hits a pothole, which knocks over all the containers of eggs. Though she is unhurt, every egg is broken. So she goes to her friend and asks how many eggs she had. Her friend says she doesn't know but she does know some things from the way she packed the eggs. When she put them in groups of 2 there was one egg left over. When she put them in groups of 3 there was also one left over. The same thing happened when she put them in groups of 4,5 or 6. But when she put them into groups of 7 she ended up with no eggs left over. How many eggs did the farmer have?