Summary: Problems Of The Week
Due March 26th
Make sure to review the guidelines before you start!
You can also look at Solutions to Past Problems on the website!
1. How many different numbers can be obtained by permuting the digits of
66644422? Make sure you explain how you got your answer.
2. All the sides of a given triangle are whole numbers. The perimeter of the
triangle is 110 inches and one side has measure 29 inches. What is the fewest
number of inches that can be the length of one of the remaining sides?
3. A merchant has determined that if the selling price of a peach is 14 cents, he will
sell 126 peaches a day. He also determined that for each cent the price is increased,
he will sell 7 fewer peaches each day. At what price, in cents, should he sell each
peach in order to maximize his daily income from peaches? Why is that the best
4. The chickens, ducks and pigs in Farmer McCoy's barn have the same number
of heads and have a total of 112 legs. How many pigs are in the barn?
5. A group of students at Parker Middle School consists of 8 students from the
6th, 7th and 8th grades. This means that their ages are between 10 and 14 . If the
product of their ages is 388,694,592 . What is the sum of their ages?