Summary: MATHEMATICAL VIGNETTES
1. An ancient Tuscan, nearing death, called in all of his sons to explain how to divide his money. First, to
his eldest son he said, "You may have one gold florin from the estate and a seventh of what remains after
that." Next, to his second eldest son he said, "Take two gold florins from what remain of the estate, and
a seventh of what remains after that." To the third son he said, "You may take three gold florins and a
seventh of what is left." In this way the old man gave each son one gold florin more than the previous son,
and a seventh of what remained, down to the last son, who got all that was left. After following their dying
father's command, the sons found that they had shared their inheritance equally. How many sons were there,
and how large was the estate?
2. An old Egyptian died, leaving his three sons 17 camels. Each camel was of slightly different value, so that
it was given a ranking from 1 to 17. Now the first son was to receive 9 camels, the second son 6, and the
third 2. How should the camels be allocated if each son is to receive the correct number of camels, but the
average rank of the camels given each son is to be equal?
3. Phidias put a pair of rabbits in a place surrounded on all sides by a wall. Assuming adequate amounts of
food, how many pairs of rabbits can be produced from that pair in a year if it is supposed that every month
each pair begets a new pair, which from the second month on becomes productive?
4. On an archeological dig on the west bank of the Nile, Masri uncovered an ancient oil lamp. Upon being
uncapped, the lamp emitted a jinni that had been bottled up since the time of the pharaohs. Granted three
wishes, Masri first said, "I would like to find the Jewel of the Nile." The jinni agreed and instantly produced
nine identical-looking stones in front of Masri. "Where is the Jewel of the Nile?" asked Masri. The jinni