Math Pathways Extra Credit
You must show all work for credit and the answer must be exactly correct.
Candies A bowl contains 75 candies, identical except for color. Twenty are red, 25 are green, and 30 are brown.
Without looking, what is the least number of candies you must pick in order to be absolutely certain that three of them are
brown?
Room Seats If 18 students occupy 3/5 of the seats in the classroom, how many students would occupy 2/3 of the
seats in the room?
Coin Sums Jada has 1 penny, 2 nickels, and 1 dime. How many different sums of money can she make, if she
uses at least one coin?
The Puzzled Driver The odometer of the family car shows 15,951 miles. The driver noticed that this number
is palindromic: it reads the same backward as forward.
“Curious,” the driver said to himself. “It will be a long time before that happens again.”
But 2 hours later, the odometer showed a new palindromic number.
How fast was the car traveling in those 2 hours?
Plus and Minus Signs
Here is the only way to insert 7 plus and minus signs between the digits on the left side to make the equation correct:
1 + 2 + 3 – 4 + 5 + 6 + 78 + 9 = 100
Can you do it with only three plus or minus signs?
Can You Get 100 Percent Savings? One invention saves 30% on fuel; a second, 45%; and a third,
25%. If you use all three inventions at once can you save 100%? If not, how much?
Rectangular Perimeter The length and width of a rectangle are
whole numbers of centimeters. Neither is divisible by 6. The area of the rectangle is
36 square centimeters. What is the perimeter of the rectangle, in centimeters?
1 to 9 Triangle The numbers 1 through 9 are placed along the sides of the
following triangle so that each side has the same sum. However, three of the nine numbers
are covered. What number is in the circle with the question mark?
Count! How many different triangles are there in the figure?
Mara Money Mara has 3 times as many dollars as her brother, Timmy. If Mara is given $20 by their mother, she
will have 7 times as many dollars as Timmy. How many dollars does Timmy have?
Houses There are 5 houses on a street: house A, B, C, D and E. The
distance between any two adjacent houses is 100 feet. There are 2
children living in house A, 3 children living in house B, 4 children living in
house C, 5 children living in house D and 6 children living in house E. If the school bus can only make one stop on that
street, in front of which house should the bus stop so that the sum of walking distance among all children will be the least?
