[10 pts] prove that if 51 integers are selected from the first hundred positive integers, (1 100), there must be a pair of these integers with a sum equal to 101. 5.

Explanation:

There are 50 pairs of positive integers that total 101:

One integer can be selected from each pair to create a set of 50 integers in the range [1, 100] such that no two will have a sum of 101. Adding any other integer from the range [1, 100], for a total of 51 integers from that range, will complete one of the sums whose total is 101.

Thus, at most 50 integers can be selected from [1, 100] such that no two will have a sum of 101, but any set of 51 integers from that range must have at least one pair that totals 101.

the most boring thing ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.