Math problems for March 29 2011

Problem #1 Arrange the digits 1, 1, 2, 2, 3, 3, as a six-digit number in which the 1s are separated by one digit, the 2s are separated by two digits, and the 3s are separated by three digits. Problem #2 Each of the boxes in the figure below is a square. Using the lines of the figure, how many different squares can be traced?

Problem #3

In a math contest of 10 problems, 5 points was given for each correct answer and 2 points was deducted for each incorrect answer.If Nancy answered all 10 problems and scored 29 points, how many correct answers did she have?

Problem #4 The perimeter of a rectangle is 20 feet and the foot-measure of each side is a whole number. How many rectangles with different shapes satisfy these conditions?

Problem #5

When Anne, Betty, and Cynthia compared the amount of money each had, they discovered that Anne and Betty together had $12, Betty and Cynthia together had $18, and Anne and Cinthia together had $10.

Who had the least amount of money, and how much was it?

Problem #6 Three water pipes are used to fill a swimming pool. The first pipe alone takes 8 hours to fill the pool, the second pipe alone takes 12 hours to fill the pool, and the third pipe alone takes 24 hours to fill the pool. If all three pipes are open at the same time, how long will it take to fill the pool?