Suggest synonyms to the following words

Simple, unsolved, familiar, to suppose, to arrange, to be divisible, a craze, world-wide, to realize.

Suggest antonyms to the following words and expressions.

Unsolved, deep problems, best known, to be famed for, insoluble, initial position.

4. Answer the questions:

1. What types of puzzles are the best-known types?

2. What was early Egyptian mathematics largely based on?

3. What is Fibonacci famed for?

4. What famous game did Cardan invent?

5. What problem was posed by Euler in 1779?

6. What was the most famous puzzle of Sam Loyd?

7. What does solving the Ernö Rubik’s cube show?

5. Contradict the following statements. Begin your answer with: “You are mistaken…, that’s not true…, I can’t agree with it…, I doubt the statement…, It’s just the other way round. Quite the reverse…”

1. Mathematical puzzles are the simplest problems which are mathematicians solve every day.

2. The best-known types of puzzles are such games as matching pennies and stone-paper-scissors.  

3. Fibonacci is famed for his invention of the sequence 1, 2, 3, 4, 5…

4. Cardan’s problem deals with seven cats and seven mice.

5. The Thirty Six Officers Problem, posed by Riemann, asks if it is possible to arrange 6 regiments consisting of six officers in a 6x6 square.

6. The most famous of recent puzzles is the one of Rubik’s square.

Translate the sentences with the modal verbs, paying attention to their meaning in each specific context.

1. The Rhind papyrus shows that early Egyptian mathematics was to be largely based on puzzle type problems.

2. To take any other off the ring next to it towards A had to be on the bar and all others towards A had to be off the bar.

3. The problem asks how 15 school girls can walk in 5 rows of 3 each for 7 days so that no girl is to walk with any other girl in the same triplet more than once.

4. We can’t but ask the more general question about n school girls.

5. The 9 cubes forming one face can be rotated through 45 .

Match the problems with the descriptions.

Egyptian problem	This problem is about the rings, which are to be taken off the bar under certain conditions.
Fibonacci’s problem	The problem deals with 15 school girls, walking in rows for 7 days.
Cardan’s problem	This problem asks if it if possible to arrange six regiments consisting of six officers each of different ranks in a 6x6 square so that no rank or regiment will be repeated in any row or column.
Euler’s problem	This problem is about a pair of rabbits in a place surrounded on all sides by a wall.
Kirkman’s problem	We are to deal with cats, mice and grain while solving this problem.

Retell the text trying to point out as many mathematical games as possible.

 

Assignments for unit III:

1. Sum up everything you now know about games and game theory and answer the following questions:

a) What is game theory? Who has found it?

b) What is a game? What types of games do you know? Give examples. Describe the rules of a game you know perfectly well.

c) What is the essence of the Prisoner’s Dilemma?

d) What is a pure strategy? Describe a pure strategy for the game of coin tossing.

e) What are the most famous mathematical games and puzzles?

 

2) Speak on the topic “Game Theory” according to the plan:

a) The definition of game theory, its connection with other sciences.

b) A game (Its definition, types, rules of some games).

c) The Prisoner’s Dilemma as a strategy.

d) Mathematical games and puzzles (give examples).

 

Try to solve

Problem 2