Ignore the answer on angel partSolutiona The minimum number

Ignore the answer on angel part

Solution

a) The minimum number of integers must be 16, the value of remainer when dividing by 15 will vary from (0 to 14) i.e. 15 values hence if we pick 16 numbers then there will be atleast one number such that the remainder value will be the same when divided by 15

b) There are 365 days in a year, considering a leap year it must have 366 days

On an average, number of birthdays per day = 2000/366 = 5.464 birthdays

Hence assuming the worst case not to satisfy the condition then there will be each day four birthdays in the next 365 days

4 * 365 = 1460 birthdays

Hence last day would have = (2000-1460) = 540 birthdays

Hence in every case there will be atleast one day with more than or equal to 5 birthdays

c) The number of lines written by programmer is equal to 500 in 17 days

The maximum number of lines that the programmer can write without fulfiilling that conditions is equal to 29 lines

29 * 16 = 464 lines

Hence on the last day, he must write atleast 36 lines to finish his work, hence there will be atleast one day when the programmer will write more than 30 lines otherwise he won\'t be able to finish the task of writing 500 lines in 17 days

d) The number of red cards in the deck of 52 cards is equal to (26 - 13 of Hearts and 13 of Diamonds), 26 cards are black (13 of spades and 13 of clubs)

In order to get atleast one red card, you need to take out atleast (26+1) = 27 cards in order to be sure that there will be atleast one red card.

Since it could be the case that the first 26 attempts will lead to the black card, now the deck contains only red cards, hence withdrawing one card will lead to atleast one card

Hence minimum number of cards must you pock is equal to 27 cards