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Combinatorics | Number Theory

Now suppose that our message units are digraphs in an N - Letter alphabet. Find a formula for the number of different affine enciphering transformations there are. How many are there when N = 26, 27, 29, 30?

Combinatorics | Number Theory

What is the largest three digit number that you can make if you use 20 stripes?

Combinatorics | Number Theory

You intercept the message "KVW?TA!KJB?FVR."(The blanks after? and R are part of the message,but the final is not.You know that a linear enciphering transformation is being used with a 30- letter alphabet, in which A-Z have numerical equivalents 0-25, blank=26, ?=27, !=28, .=29.You further know that the first six letters of the plain text are "C.I.A". Find the deciphering matrix A inverse and the full plain text message.

Combinatorics | Number Theory

Question

A 33-term series is written using only the integers +9 and −2. How many such series can be written that have a sum of0?

Answer

The number of series that can be written is 1 107 568.

Request and Details

Can you please provide a process for solving this question? It may involve permutations and combinations.

Combinatorics | Number Theory

1.1 On which very old object does a table of prime numbers appear?

Combinatorics | Number Theory

Number of ways an animal can travel from A to C via B, if there are 3 routes from A to B and 5 routes from B to C

Combinatorics | Number Theory

For the function: F(W,X,Y,Z) = "\\prod" M(0,3,4,6,7,9,11,15):

a) identify the essential prime implicants

b) Write the minimal sum

Combinatorics | Number Theory

with the aid of an example, explain how even and odd parity work and give an example application where they may be useful.

Combinatorics | Number Theory

For the functions below:

i) G (W,X,Y,Z) = Σm (1, 4, 7, 8, 9, 11) + d (0, 3, 5)

ii) F (A, B, C, D) = Σm (7, 9, 12, 13, 14, 15) + d (4, 11)

iii) F (A, B, C, D) = πM (2, 8, 11, 15) + d (3, 12, 14)

iv) F (W, X, Y, Z) = πM (0, 2, 6, 11, 13, 15) + d (1, 9, 10, 14)

a) Identify the essential prime implicants

b) Write the minimal sum/product

c) Implement with NAND gates only

d) Implement with NOR gates only

Combinatorics | Number Theory

Draw the multiple-level NOR circuit for the following expression: CD(B + C)A + (B"\\bar{ C}" + D"\\bar E" )