Construction Projects

A particular construction crew places orange barrels on both sides of a road that is under construction such that the centers of adjacent barrels on the same side of the road are 15 feet apart. If the crew does this for a 1.5 mile stretch of roadway, how many barrels will be placed on the two sides of the road in total?

Martin Luther King, Jr. Day

Dr. Martin Luther King, Jr., a civil rights activist whose passion and leadership led to great cultural changes in America, was born on January 15, 1929. On November 2, 1983, President Ronald Reagan signed a bill to create a federal holiday honoring Dr. King. The national holiday celebrating the birth of Dr. King was first observed on January 20, 1986. Every year since, Martin Luther King, Jr. Day has been observed on the third Monday of January.    

What is the earliest date in January that Martin Luther King, Jr. Day can occur?

Prime Number Sense

If n is the sum of three consecutive primes and is also the product of two 2-digit primes, what is the least possible value of n?

Let’s try the two 2-digit primes of least value, 11 and 13. These primes have a product of 143, and 143/3 is around 47. Two primes close in value to 47 are 43 and 53. So we try the sum 43 + 47 + 53 and see that it does, in fact, equal 143.