# Tag Archives: programming

## Combinatorial Game Theory VII

Lesson 7 [ Warning: another long post ahead. One of the proofs will also require mathematical induction. ] In this lesson, we will see how some games can be represented by numbers (which can be integers or fractions). We will also … Continue reading

## Combinatorial Game Theory VI

Lesson 6 General Combinatorial Game Theory [ Warning: the following lesson is significantly longer than the previous ones. ] Starting from this lesson, we will look at a more rigourous, complete and general theory. Prior to this, in any game configuration both … Continue reading

## Combinatorial Game Theory V

Lesson 5 We did mention in the first lesson that CGT covers games without draws. Here, we’ll break this rule and look at loopy games, i.e. games with possible draws. [ To be specific, loopy games are those where it’s … Continue reading

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## Combinatorial Game Theory III

Lesson 3 We’ve learnt Nim and we’ve learnt the Square Game. Now, let’s combine them and consider the following game, which we shall name Nim Square. Start with r heaps of stones, of sizes . Play alternates between two players: at … Continue reading