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Problems(2)
a ladder rests against a vertical wall (2017 Auckland MO J1)
Source:
12/31/2020
A meter ladder rests against a vertical wall. The midpoint of the ladder is twice as far from the ground as it is from the wall. At what height on the wall does the ladder reach?
geometryright angle
more parents than children in the building? (2017 Auckland MO S1)
Source:
11/15/2021
In an apartment block there live only couples of parents with children. It is known that every couple has at least one child, that every child has exactly two parents, that every little boy in this building has a sister, and that among the children there are more boys than girls. You may also assume that there are no grandparents living in the building.
Is it possible that there are more parents than children in the building? Explain your reasoning.
combinatorics