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Joy of Problem Solving

Intro to Problem Solving

Joy of Problem Solving: Logical Reasoning

           

If all of the statements are true, where is the gold?

There is gold in only one of the chests. If only one of the messages is true (and the other two are lies), where is the gold?

In the previous two problems, we were given imperfect information and had to come up with creative ways to use the information given to solve the problem.

In this chapter, we explore the idea through many math problems that require this mix of creativity and logic.

In the above image, there are 2 squares of different sizes.

What is the minimum number of matchsticks that we have to move to create 3 squares?

Note: The squares may or may not be of different sizes.

From the above diagram, we see that in order to create 1, 2, 3 and 4 congruent unit equilateral triangles on a flat plane, we need 3, 5, 7 and 9 matchsticks respectively.

What is the minimum number of matchsticks on a flat plane needed to create 7 congruent unit equilateral triangles? (Be careful! This one is trickier than it initially looks.)

What is the minimum number of matchsticks that can be removed to leave three non-overlapping squares of the same size, without any matches left over?

Remember: Every remaining matchstick must be part of at least one of the three squares.

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