Combinatorics | Number Theory Answers

AN OFFICE SECRETARY TRIES TO DEVICE CODING SCHEME FOR CERTAIN RECORDS, USING DIGITS 1 TO 4. SHE WANTS TO FIND THE TOTAL NUMBER OF CODES OF DIFFERENT DIGITS. IF ONLY THREE OF THE FOUR DIGITS ARE USED

A pro baseball team is having a promotion in which every tenth fan that enters the stadium gets a free hat and every 12th person gets a free t shirt. How many fans will come into the stadium before a fan receives a hat and a t shirt?

Suppose you decide to represent the cards in a standard deck using the numbers 1 through 52. So for this, the cards are arranged so that the clubs come first, then the diamonds, then the hearts and then the spades. Also within a suit, the order of the cards is ace, then the cards 2 through 10, then the jack, then the queen, then the king. So after arranging the cards in this manner, the ith card is assigned the number i. Thus the king of spades will get the number 52, and the ace of clubs the number 1.

1.What number does the 9 of spades get?

2. Suppose some card has number n. I would like to know if it is a diamond. Which of the following tests will tell me if this is the case?
Options

1.n > 26

2.ceiling(n/4) = 2

3. n mod 13 = 0

4ceiling(n/13) = 2

some friends bought some chocolates and hide them in a box and went to sleep. one of the friends wake up and ate one chocolate before taking half the number of chocolates ,now the second friend wake up did the same and went to sleep this process continued until the last person did the same and went to sleep when they woke up in the morning only one chocolate was left, if it is known that there are less than hundred chocolates then how many friends are there to the maximumwas left if it is known that there are less than hundred chocolates then how many friends are there (to the maximum)

Secrets of pascal triangle

What are sexy prime numbers?

In how many ways can 8 people be seated on a bench if 3 particular people must sit together?

from 24 to 12943 how many numbers can be made such that 1,3,5 does not appear 3 or more than 3 times

How many integers are there in between 1 and 500 divisible by 3 or 5

If n is greater than or equal to 9, and n-2 and n+2 are both primes, then 3|n.