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In 1925, two 25-year-old couples discovered an island of 1 square kilometer. There was a fine spring of fresh water, the soil was rich, there were fish in the sea and many trees to use for fuel and building. They decided to live there and raise families. After a time each couple had four offspring who married the children of the other couple and who in turn had four children of their own. In 1975 they had a party to celebrate the 75th birthdays of the grandparents. "How many we have grown to be!" said the old people proudly as they counted the________ (ans. 28) people gathered together. "just think," said the grandchildren, many of whom were already married and about to start their families, "if we have the same number of children as our grandparents and parents, by the year 2000 there will be________(ans. 56) people living on the island. And if our children marry and each couple has four children, then on our 75th birthdays in 2025, there will be________ (ans. 112) people at the party. The grandparents began to look worried. "The most that this island could support would be 96 people and even then it would be crowded and difficult," said one. "With more people there would not be enough water or land to grow the food needed." "The fish are getting scarce and we have already cut down half the trees". "Now, let's see, the question is: How many children can each couple have and still keep the total population under 96 people? Using 96 pebbles, they put down on the ground first four to represent the original parents, then eight to indicate their children, then 16 for the children's children. All these (28) were at the party. Next with all the pebbles, they figured out how many people would be living on the island in 2000, 2025 and 2050 if each couple had four, three, or two children. Each time the sum of the last three generations reached more than 96, they began again with less children. "We certainly can't keep on having four children." "Cutting down to three children won't help for long either." They finally decided that if the population was to go no higher than 96, beginning in 2000 couples should average_________ (ans. 2) children a piece.
Everyone at the party was glad the danger had been discovered in time. They began the birthday feast. "It certainly will be very different when there are so many people living on the island," said the grandparents. "We'll have to live very carefully," said the parents. "...and share equally," added the children. "The harvest can no longer be divided so 1/3 of us get 800 baskets of grain and the rest of us only 160, the way we've been doing." Everyone stopped eating and began calculating again.
By harvest time this fall two babies will have been born so we'll be 30 people.
"Two and a half baskets are not enough to live on!" "Let's see how much each person would get if we have equal shares." If 96 persons share 960 baskets, then one person will have________(ans. 10) baskets "it would be a big change, but no one would starve," they decided.
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