The riddles of Cleopatra

LONG ago in Egypt, lived a beautiful, but arrogant queen named Cleopatra. Though Egyptians had not heard of zero, they had developed a highly advanced system of mathematics by the Old Babylonian period of about 2000 BC. Thousands of mathematical tablets of that era that have been found, show that Egyptians had an impressive knowledge of arithmetic, linear and quadratic equations and geometry. Cleopatra, too, like most learned persons of her time, had inherited this knowledge and memorised tables of multiplication, squares, square roots, reciprocals and common constants. With the growth of her intellect and ambition, her reputation also spread. Julius Caesar, dictator of Rome, also heard of her beauty and talent.

"Anthony," says Caesar, "I want to go there, see her and conquer her." Mark Anthony, his friend and General, says, "Take the number of your fingers multiplied by the number of you toes divided by one half and add it to the number of months in a year.

 What do you get?" "Why do you ask that now," says Caesar, "when we are discussing things that are more important?" "I ask this because, if you can’t solve this problem, you should forget about conquering her," says Anthony.

"Let us see, 10x10=100 and 100÷1/2=200 and 200+12=212, simple, isn’t it?" says Caear. "Right, let us sail for Egypt," says Anthony.

Egypt: Caesar and Cleopatra are sitting across a table. Caesar decides to break the silence. "Tell me about your family?" Caesar asks her. "My mother and father have six sons and each son has one sister," says Cleopatra. "I see, you have 11 members in your family, that’s a big number. I hope your sisters are just as beautiful as you," says Caesar. "Excuse me, but my family has nine members and I am the only daughter of my parents," says Cleopatra.

An arena in Egypt: The visiting team from Rome has just won a tug-of-war match against Egyptian troops. There are nine players on each team and now they want to congratulate each other. They begin shaking hands and each player only shakes hands with every other player just once. Cleopatra says, "I wonder how many times did the players shake hands?"

"The first player shook hands with 8 other players of his team, while the second player shook hands with 7 other players. This is because he had already shaken hands with the first player. The third player shook hands with only 6 players as he had already shaken hands with the first player and second player. This continued until the last player had only one possibility left. Therefore the number of handshakes was 8+7+6+5+4+3+2+1=36," says Mark Anthony. "General! I didn’t know you were here," says Cleopatra, "I am sure Caesar could not have surprised me like that. I am glad you are here." "Call me Anthony," says the General.

Cleopatra’s private chambers: Cleopatra is with her childhood friend Iris. "I would love to see greatest swordsmen in the world fight for the right to marry me. I should invite 100 gladiators for this contest. The loser in each match will be eliminated from the contest, because the finish will be to the death," says Cleopatra. "How many matches will be played to determine the winner?" says Iris.

Cleopatra says, "If there is to be only one winner, there will be 99 losers and, therefore, 99 matches. In round 1, there will be 50 matches to produce 50 winners, round 2 will have 25 matches to produce 25 winners and round 3 will have 12 matches to produce 12 winners. This is because one person out of the 25 winners will have to wait until later to fight again. Round 4 will have 6 matches to produce 6 winners, round 5 will have 3 matches to produce 3 winners and round 6 will have 2 matches. The gladiator left out before will now play to make it an even field. This will produce 2 winners, who will fight for the ultimate prize — Cleopatra. Count the number of matches in each round: 50+25+12+6+3+2+1=99." Iris says, "That is a big bloodbath. Are you sure Mark Anthony will live through this to win you?" "Yes, and he shall defeat Caesar in the final," says the queen of Egypt, "Romans have always amazed me. Do you know how can 12 be 7?" "No," says Iris. "When 12 is a Roman numeral (XII). Cut off the top and you get VII," says Cleopatra and breaks into a wild laugh.

Things go wrong. Caesar is assassinated withing 15 days of entering Rome. Anthony defeats the conspirators led by Brutus, but is defeated in the battle of Actium by Octavius and chased out of Rome. Octavius sails for Alexandria in Egypt to conquer Cleopatra, who with Anthony, has been surrounded by Roman troops.

Cleopatra’s chamber: "Oh Anthony! When things go wrong, what can you always count on?" says Cleopatra. "Love, my dear," says Anthony. "Your fingers, fool," says Cleopatra.

— Aditya Rishi