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20 February
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Please provide handwritten solutions to the following 3 puzzles.
From the book, pages 28-32, do problem 2 on the politicians, and do problem 13
on the tea party.
Third, solve the problem of the farmer, the wolf, the goat, and the cabbage.
In this puzzle, a farmer wants to move a wolf, a goat, and a cabbage across
the river.
His boat allows him to move only 1 item at a time.
If left alone, the goat eats the cabbage, and the wolf eats the goat.
How can the farmer get all across the river unharmed?
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21 April
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Please provide handwritten solutions to the following puzzles.
- Consider the Monty Hall problem with 4 doors, numbered 1, 2, 3, and 4.
Perform 10 times the following experiment.
First, play Monty Hall by randomly putting a prize behind one of the 4 doors.
Second, pretend to be a guest who picks a door in the hope of getting the
prize.
Since the guest supposedly does not know where the prize is, you randomly pick
one of the 4 doors.
Third, play Monty Hall again by opening 2 of the remaining 3 doors behind
which there is no prize.
Four, count whether it is better to switch doors from the guest's original
choice to the only other closed door.
- Now, in the 4-door Monty Hall puzzle, compute the exact chance of the
prize being behind the door originally chosen, and the chance of the prize
being behind the other door.
Justify your answer.
Does your earlier 10-fold numerical experiment support this mathematical
result?
- Consider the following variation on the Monty Hall problem with 4 doors.
Perform 20 times the following experiment.
First, play Monty Hall by randomly putting a prize behind one of the 4 doors.
Second, pretend to be a guest who picks a door in the hope of getting the
prize.
Since the guest supposedly does not know where the prize is, you randomly pick
one of the 4 doors.
Third, pretend to be a storm which random opens 2 of the other 3 doors.
Four splits into two subcases.
Subcase one of four, if you open a door where the prize is (this now can
happen!), then record this case as a blank.
Subcase two of four, if the two doors you opened do not reveal the prize, then
count whether it is better to switch doors from the guest's original
choice to the only other closed door.
Also keep count of the total number of non-blanks.
- Now, in the variation on the 4-door Monty Hall puzzle, compute the exact
chance of the prize being behind the door originally chosen, and the chance of
the prize being behind the other door, but restrict yourself to the situation
where the two open doors do not reveal the prize.
Justify your answer.
Does your earlier 20-fold numerical experiment support this mathematical
result?
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