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21 May 2005: 20. A space-filling curve (Exercise 14, Chapter 7 of Rudin’s book).

21 May 2005: 20) Let G have n r 1 vertices and tr1(n) 1 edges.(i) Prove that for every p in the range r p n, G has a subgraph of order

18 Oct 2005: 4 ANALYSIS II EXAMPLES 1. 20. A space-filling curve (Exercise 14, Chapter 7 of Rudin’s book).

27 Oct 2005: 20) (i) Construct a [7, 8, 4]-code from Hamming’s code.(ii) Prove that A(n, d) 2A(n 1, d).(iii) Prove that if d is even then

21 May 2005: Show that satisfies the triangle inequality. Is it a metric? 40) Rephrase your solution to Question 20 (on coin weighing) in terms of conditionalentropy.

14 Mar 2005: 20. graphs G(X,Y ), G(Y,Z) and G(Z,X) with densities p, q and r and let G be the tripartite.

21 May 2005: 20. An n n magic square is a square matrix whose rows, columns and two diagonals all sum to the samequantity.

30 Jan 2005: 0, 3, 1, 4, 7, 10, 13, 16, 19, 57, 60, 20, 17, 14, 11, 8, 5, 2, 6, 9, 12, 15, 18, 21,24, 27, 30, 33, 36, 39, 42,

12 Apr 2005: ThenBB f. B(ω) is. 20. non-zero only if HC(ω) = 1 for every C K1.