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This page contains syllabus, class and homework problems and solutions to the problems. New material will be added about once in a week. Check for updates. |
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February 6
In class: We learn how to pave the floor using tiles of
tricky shape and devise different tilings. Note that your tilings should work for the unbounded floor (in other words,
you should understand how to continue your tiling in all directions for long distances but you should not care about walls).
It helps if your tiling has some order in it (so that it looks the same at different places).
We also count small cubes in solid figures and solve some
puzzles.
Homework 2, due February 13
Solve all problems that you have not solved in class.
February 13
In class: We solve
logical problems. These
problems are based on the following fairy tale. Once upon a time there was a king who had many beautiful
daughters. There were many dangerous tigers in his kingdom as well.
A knight came to the king. He wanted to marry a princess.
The king decided to test how clever the knight was. He offered the following test.
There were two doors leading to two rooms. In each room, there was a princess OR
there was a tiger (a room can not be empty). The problem was to decide which door leads to a princess
(and go through that door, if the knight preferred a princess to a tiger).
The king placed labels on the doors to help the knight to choose.
These labels could be true or false. Note that tigers could be in both rooms (very unlucky) OR princesses could be in both rooms (very lucky) OR a tiger could be in one room and a princess in the other (in this case everything depends on you).
We also solve problems by trial and error method. See the solution to the first problem in
the list of problems to understand the idea.
Homework 3, due February 20
February 20
In class: We solve logical and
arithmetical problems.
Homework 4, due February 27
Solve the problem marked as homework.
February 27
In class: We solve geometry problems about
cutting a pie.
Homework 5, due March 6
Solve the problem marked as homework.
March 6
In class: We study binary system.
Homework 6, due March 13
March 13
In class: We construct magic squares and solve arithmetical
problems.
Homework 7, due March 20
Solve all problems marked as homework.
March 20
In class:
We cut different geometric figures into two, three or four equal pieces. Two pieces are equal if you can put one
onto the other so that they coincide.
Homework 8, due April 3
Solve all problems marked as homework.
April 3
In class: We do geometry with matches. We also count triangles.
Homework 9, due April 10
April 10
In class: We solve different optimization problems.
Homework 10, due April 17
Do all problems marked as homework.
April 17
In class: We solve puzzles with numbers and compute areas
of different figures.
