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After hiking for a couple of hours I got hungry, so we unpacked the chocolate (which was lucky for us since it was already half molten) and the others started to discuss the best way to divide the chocolate between the five of us. "I know!" my Prince said triumphantly. "Since we are five people and we have five bars of chocolate, let's just give one bar to each person!" "Oh, what a bore!" exclaimed Rapunzel. "We don't want to divide the chocolate up in the easiest way, we want to find the mathematically most interesting way." (And to the me she said, "Next time you have to take someone prisoner, be sure to take a genius and not a prince, OK?")
"No!" cried the prince, "I want to be number one!" "I have an even better idea," came Queen Dido. "My ancestors, the Egyptians, were faced with a similar problem almost 4000 years ago. Their solution was to give each person one fourth of a bar more than the person before." "But I want to be number one!" cried the prince. "OK," was Dido's reply. "And I'll be number five. Rapunzel, you'll be number two, you Dragon will be number three and Joe'll take four. OK?" "OK," I quickly replied to make an end to this whole thing. "In that case I get exactly one chocolate bar." And before there could be any further discussion, I ate my share so they had to be happy with theirs too. Can you help the Prince find out how big his share is? Do you need a hint? |
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