Which height was chosen by the most students?
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“I guess the flagpole will be 25 feet tall,” said Mrs. Jewls. “Since more people chose that height than any other.”
g
(I know. I just gave away the answer to problem 38, but it was a pretty easy question.)
g
“Hey that’s not fair,” said Jenny. “ ‘A hundred feet’ came in second! There should be a vote between ‘twenty-five feet’ and ‘a hundred feet.’ ”
“That sounds fair,” agreed Mrs. Jewls.
PROBLEM 39
They voted. Each student had to vote for either “25 feet” or “100 feet.”
Naturally each child voted for the number that was closer to his or her original choice. For example, Eric Bacon voted for “100 ft.” because 91 is closer to 100. Stephe
n voted for 25 ft. because it was closer to 6 ft.
What was the outcome of the vote?
“So that will be the height of the new flagpole,” said Mrs. Jewls.
“But that’s not fair!” said Terrence. “Four people liked ‘85 feet.’ We’re entitled to a vote too.”
“I guess you’re right,” said Mrs. Jewls.
PROBLEM 40
There was another vote. This time it was between “the winner of problem 39” and “85 feet.” Again each child voted for the number closer to his or her original choice. What was the outcome of this vote?
“We should compromise,” said Bebe and Calvin. “Fifty feet is right in the middle. If we get a fifty foot flagpole everyone will be happy.”
“Let’s vote,” said Mrs. Jewls.
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PROBLEM 41
This time everyone voted for either “50 feet” or “the winner of problem 40.” What was the outcome of this vote?
As you might guess, everyone in the class demanded that his or her number be given a fair chance. So they continued having elections. It was very much like a game of tether ball at recess. After each vote, another number was given a chance to “play the winner,” until at last every number was voted upon.
PROBLEM 42
In every vote, between any two heights on the chart, it turned out that one child always voted for the height that won. Who was that child?
PROBLEM 43
What will be the height of the new flagpole? (Which height wins against any other height?)
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