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MathMagic Cycle 16: Level 10-12 Regular

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Lewis Carroll (Alice in Mathland?) was not only a very talented writer,
but he was quite fond of mathematical puzzles. The following is attributed
to him:

     "A queen and her son and daughter are being held captive in the top
room of a high tower. Outside their window is a pulley with a rope over
it, and a basket at each end of the rope. The baskets are of equal weight.
The one outside the window is empty, and the other on the ground contains
a stone with a mass of 30 kilograms. The stone serves as a counterweight.

     There is enough friction in the pulley so that it is safe for anyone
to be lowered in one basket provided his or her mass is not greater than
the mass of the other basket by more than 6 kilograms. If the difference
is greater than six kilograms, they come down with such speed that the
bump at the bottom might injure them. Of course, when one basket goes down
the other basket goes up to the window.

     The queen's mass is 78 kilograms, the daughter's is 42 kilograms, and
the son's is 36 kilograms. What is the simplest algorithm (fewest number
of steps) by which they can all get safely to the ground? The basket is
large enough to hold any two people, or one person and the stone. No one
assists the prisoners in escaping, nor can they help themselves by pulling
on the rope. In other words, the pulley operates only when the mass in one
basket exceeds the mass in the other."

Assuming the last person gets out of the way quickly, make a diagram of
the movements (____down; _____up) - What is the algorithm Carroll is
after?

(from Aha! Insight by Martin Gardner)

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MathMagic Cycle 16: Level 10-12 Advanced

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Cards ahoi

Develop with your NTP a method to predict how many cards you must draw
from a 52 card deck to make sure you have 7 cards of a matching suit.

Along the same lines, what is the probability that you will get seven
cards of the same suit if you draw from 7 to 24 cards without replacing
each card after it is drawn.
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