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GCSE: Beyond Pythagoras

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1. Towers of Hanoi Investigation

While moving the discs you can not put a bigger disc on top of a smaller one. We are to try with different numbers of discs and see if you can find a rule or a pattern Number of discs and its moves 1 Disc 1. 1-B 2 Discs 2. 1-B 3. 2-C 4. 1-C 3 Discs 1.

• Word count: 383
2. Investigate the probability of someone rolling a die and the probability of it landing on particular number for a player to win the game

= 1- (5 x 2 x 1) 6 3 2 P (LLL) = 1 - 5 18 P (LLL) = 13 18 I also found the probability of A, B and C winning in Round 1: P (A) wins = 1 6 P (B) wins = 5 x 1 = 5 6 2 18 P (C) wins = 5 x 2 x 1 = 5 6 3 2 18 In the second round the probabilities of winning will be different, as you must say that no one won in the last round. This is how I found out the probability of A, B and C winning in the second round: P (A)

• Word count: 1482