## Daily Routine

One of my high school instructors used to have a saying, “Early is on time, on time is late, and late is left”. It is a saying that I bought into many years ago, and something that I do my best to follow. In Ghana, we hold our students to that same standard. Despite daily pleas for us to recognize GMT (Ghana Man Time) students are marked late if they arrive after 8:30 AM.

By 8:45 each morning students are presented with a daily challenge problem that they may solve before their 9am class, or wait for the solution to be presented to the group before the 1:00 PM design project.

Most of the challenge problems from the past two weeks are listed below. We will do our best to post the new problems and solutions to our blog and facebook pages moving forward. Enjoy!

1)

A person has two strings, each of which burns for one hour. Assuming that the strings burn at non-constant rates, how does one measure 45 minutes?

2)

A person has two water jugs. The first jug has a volume of 500 ml. The second jug has a volume of 300 ml. Using the two jugs and an endless supply of water, how can they measure exactly 400 g? You may neglect the weight of the jugs.

Hint: Assume 1g = 1ml = 1cm(^3).

3)

What is the sum of all the numbers, one to one million?

4)

There are three bags of gold. One of the bags contains fake gold. All the bags and all the coins look exactly alike. There is the same number of coins in each bag. The real coins weigh only one ounce each, the fake coins weigh 1.1 oz. apiece. You have a one-pan penny scale and one penny, which means you can weigh something just once. (You load the scale, put the penny in, an the scale spits out a piece of paper with the weight.) How can you tell which bag has the fake gold?

5)

Have a friend select a number 1 through 100 and write it down. What is the minimum number of yes or no questions required to guarantee that you have guessed the correct number?

6)

What is the probability that the last day of a leap year is a Sunday?