Combinatorics | Number Theory Answers

Using Polya's method

Consider the street map. Trisha wishes to walk directly from point A to point B. How many

different routes can she take if she wants to go past Starbucks on Third Avenue?

Find a pair of numbers that provide a counterexample to show that

the given statement is false.

(a) If the sum of two counting numbers is an even counting number, then the product of the two counting numbers is an even

counting number.

(b) If the product of two counting numbers is an even counting

number, then both of the counting numbers are even counting

numbers.

lan's Cafà ƒ © and Restaurant is offering a promo. They charge PHP 250 per person for a group of five. If the group has more than five persons, the first five persons pay the same and the rest shall pay PHP 100 each. A group of more than five people decided to divide the bill equally amongst themselves. How many people were in the group if each of them paid PHP 130?

Find the least multiple of 23, which when divided by 18, 21, and 24 leaves the remainder 7,10 and 13 respectively.

Bazil wrote two numbers in his notebook, {2}^{12}{3}^{2}{5}^{7}{7}^{5} and {2}^{3}{3}^{12}{5}^{2}{7}^{2}. After that he proceeded writing numbers in the notebook according to the following rule. Each time he can write down a positive number equal to the difference of any two numbers already written in the copybook. It is not allowed to repeat the numbers in the notebook. Find the sum of two smallest numbers that can be obtained in the notebook.

1.      A tailor wants to make square shaped towels. The required squared pieces of cloth will be cut from a ream of cloth which is 20 meters in length and 16 meters in width.

a)     Find the minimum number of squared pieces that can be cut from the ream of cloth without wasting any cloth.

b)     Briefly explain the technique you used to solve (a).

Find out if the inverse exists for the following, give reasoning behind your answer. If you conclude that the inverse exists then find the Bezout coefficients and the inverse of the modulo.

(a) 678 modulo 2970

(b) 137 modulo 2350

Find out if the following numbers are prime numbers, show your work:

(a) 773

(b) 733

(c) 377

there are 14 blue and 28 red bulbs to be used for a birthday party. they are to be placed in a plastic bag so that each bag contains the same number. what is the largest plastic bag will be needed

Bazil wrote two numbers in his notebook, {2}^{12}{3}^{2}{5}^{7}{7}^{5} and {2}^{3}{3}^{12}{5}^{2}{7}^{2}. After that he proceeded writing numbers in the notebook according to the following rule. Each time he can write down a positive number equal to the difference of any two numbers already written in the copybook. It is not allowed to repeat the numbers in the notebook. Find the sum of two smallest numbers that can be obtained in the notebook.