The tiny state of Crambodia has only 12 inhabitants, and is governed by the Council of Twelve, which consists of all citizens and passes legislation only when at least 11 citizens vote in favour. Recently, the Council of Twelve was debating the distribution of wealth among Crambodia's citizens.
"Fellow Crambodians," said the poorest citizen, Penny Less, "it is manifestly inequitable that my total worth should be exactly one Crambodian doubloon, when the richest among us is worth more than 2,000 times as much!"
"I agree," said the fourth richest citizen, Lotta Cash. "But what should we do to even things up?"
"I propose that the wealthiest citizen should be required to double the wealth of all the other citizens," said Penny.
"I would argue strongly against that," said Midas Moneybags, who was the wealthiest citizen.
"Yes, but you would, wouldn't you?" said the second poorest citizen, Job Churchmouse. "I second Penny's motion!"
The motion duly passed, 11 votes to one. But when the money was transferred, only the owners of the fortunes concerned had changed—the amounts were exactly the same as before.
How many doubloons did the wealthiest citizen own?
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The answer
The wealthiest citizen owned 2,048 Crambodian doubloons. When Penny's wealth is doubled, it increases from one doubloon to two. So someone else—Job Churchmouse—must originally have owned two doubloons. When Job's wealth is doubled he has four doubloons, which means there must have originally been someone else with four. By the same reasoning the other citizens had 8, 16, 32, 64, 128, 256, 512, 1,024 and 2,048 doubloons. Midas Moneybags pays out a total of 2,047 doubloons, reducing his wealth to one doubloon, and everyone else moves one step up the financial ladder.
The winner was David Esparza from Cheshire
