Problem of the Week Solution Archive
Problem of the Week #17
What time is it? The digits on this clock add up to 6. How many times during one day (24 hours) will the numbers add up to 6 happen? Show your work using pictures, numbers or symbols. Prefer to work it out by hand? Download the paper copy here. 
SOLUTION
The digits on the clock will add up to 6 seventytwo times per day. Times for am and double for pm: 12:03, 12:30, 12:12, 12:21 1:05, 1:50, 1:32, 1:23, 1:14, 1:41 2:04, 2:40, 2:22, 2:31, 2:13 3:03, 3:30, 3:12, 3:21 4:02, 4:20, 4:11 5:01, 5:10 6:00 10:05, 10:50, 10:23, 10:32, 10:14,10:41 11:22, 11:04, 11:40, 11:31, 11:13 
Problem of the Week #16
Balloon Auction For Pierce’s 2015 Spring Fundraiser on May 16th, the PTO ordered 23 blue balloons, 18 red balloons and 19 yellow balloons for the balloon auction. When the order arrived, they realized they had only received half of the balloons. How many balloons did they receive? Show your work using pictures, numbers or symbols. Prefer to work it out by hand? Download the paper copy here. 
SOLUTION
The PTO received only 30 balloons 


SOLUTION
There are 10 other dates in 2015 that can be written as palindromes. (51015, 51115, 51215, 51315, 51415, 51515, 51615, 51715, 51815, 51915) 
Problem of the Week #14 Row, Row, Row Your Boat You are rowing up a river to reach a town 85 miles away. You can make 15 miles a day, but at night, while you are sleeping, the current pushes the boat 3 miles back downstream. If you set out first thing Tuesday morning, on which day will you arrive? Due on Tuesday 4/14 Show your work using pictures, numbers or symbols. Prefer to work it out by hand? Download the paper copy here. 
SOLUTION
The answer to: "Row, Row, Row Your Boat" is that the boat will arrive at the destination the following Monday. (Note: Tuesday will also be accepted as an answer, as the boat will be pushed downstream Monday night.) 
Problem of the Week #13
Folded Square If you fold a square piece of paper vertically, the new rectangle has a perimeter of 36 inches. What is the perimeter of the original square? Challenge: What is the difference between the area of the original square and the area of the new rectangle? Due on Tuesday 3/31 Show your work using pictures, numbers or symbols. Prefer to work it out by hand? Download the paper copy here. 
SOLUTION
The perimeter of the original square is 48 inches. CHALLENGE ANSWER: The difference between the area of the original square and the new rectangle is 72 square inches. 
Problem of the Week #12
An Odd Sum An example of consecutive odd numbers is 1, 3, 5. Find three consecutive odd numbers with a sum of 111. Show your work using pictures, numbers or symbols. Prefer to work it out by hand? Download the paper copy here. 
SOLUTION
The consecutive odd numbers 35,37, and 39 have the sum of 111. 
Problem of the Week #11
Building Blocks Each figure above is formed by surrounding one row of black squares with white squares. How many white squares will surround one row of 10 black squares? Show your work using pictures, numbers or symbols. Prefer to work it out by hand? Download the paper copy here. 
SOLUTION
26 white squares will surround 10 black squares. 
Problem of the Week #10
The 100th Day Potato Challenge A Farmer grows 100 pounds of potatoes. He sells them to a grocer who will divide them into 5pound bags and 2pound bags. What is one combination of bags the grocer could make using all 100 pounds of potatoes? Can you find more possible combinations? Show your work using pictures, numbers or symbols. Prefer to work it out by hand? Download the paper copy here. 
SOLUTION
There are multiple solutions of 2lb bags and 5lb bags that total 100. For example, ten 2lb bags and sixteen 5lb bags have a total of 500 lbs. See chart: 
Problem of the Week #9
That's a lot of Nickels! One nickel is about 2 millimeters thick. If we had a stack of nickels 1 meter high, how much would it be worth? Hint: How high would a stack of 5 nickels be? Show your work using pictures, numbers or symbols. Prefer to work it out by hand? Download the paper copy here. 
SOLUTION
500 nickles is 100 cm. so 1 meter of stacked nickles is worth $25.00. 
Problem of the Week #8
Happy New Year It’s 2015! To celebrate the New Year, kindergartners are going to count to 2,015. It takes 1 second to say each number. If they start at 8:00am, will they be done counting before lunch? Show your work using pictures, numbers or symbols. Prefer to work it out by hand? Download the POW here. 
SOLUTION
Yes, the kindergarteners should be done in less than an hour. 

Problem of the Week #6
You Go Girls In a group of 25 girls, 8 ran for the cross country team, 13 are on the math league team, and 6 are on both teams. How many of the girls are not on either team? Show your work using pictures, numbers or symbols. Prefer to work it out by hand? Download the paper version here. 
SOLUTION
10 girls were not on either team. 
Problem of the Week #5
Fruit Stand At a fruit stand, an apple and a pear cost 25 cents, a pear and a banana cost 19 cents, and an apple and a banana cost 16 cents. Alex uses two of his coins to buy and apple. All together he buys one apple, one pear, and one banana. How much does Alex spend? Show your work using pictures, numbers or symbols. Prefer to work it out by hand? Download the paper version here. 
SOLUTION
Alex spent 30 cents at the Fruit Stand. 
Problem of the Week #4
UNICEF: How much money did Pierce collect? In 2013, Pierce students collected change for UNICEF on Halloween. When the boxes were emptied by 1W students and the money was sorted there were:
What is the total amount of money Pierce collected? (You can use a calculator, but be sure to record your equations.) Prefer to work it out by hand? Download the paper version here. 
SOLUTION
The students of Pierce collected $1040.74 Great job everyone! 
Problem of the Week #3
Better Luck Next Year! The Red Sox finished their season last week. At the end of the last game the 10 players and 4 coaches all shook hands with each other. How many handshakes were there? Show your work using pictures, numbers or symbols. Prefer to work it out by hand? Download the paper version here. 
SOLUTION
There were 91 handshakes. 
Problem of the Week #2
Boxed In A cubical box without a top is 4 cm on each edge. It contains 64 identical 1cm cubes that exactly fill the box. How many of these small cubes actually touch the box? Show your work using pictures, numbers or symbols. Prefer to work it out by hand? Download the paper version here. 
SOLUTION
There are 52 cubes that touch a side of the box. 
Problem of the Week #1
Elevator Ride Jackie, our beloved custodian, got a new job at Towers High School. He began his day in the basement. He took the elevator up 20 floors to fix a light. Then he took the elevator down 8 floors to repair a broken window. Next he went up 7 floors to have lunch in the cafeteria. The floor with the cafeteria is the halfway point in the building. How many floors are in Towers High? Show your work using pictures, numbers or symbols. Prefer to work it out by hand? Download a paper copy here. 
SOLUTION
The solution could be 37, 38 or 39, depending on how the problem was interpreted. Based on the clues, the halfway point is floor 19. If you add 19 + 19, then the building has 38 floors. If you believe that from floor 19, there are 18 floors above and 18 floors below, then the answer is 36 + 1 (for floor 19) or 37. And if you remembered to include the basement as a floor, then the answer could be 38+1 = 39 or 37 + 1 = 38. 
20132014 Solution ArchiveProblem of the Week #17

SOLUTION
Part A: If Anna has 12 dimes and 3 nickels, she would have 15 coins and $1.35 Part B: If Royce has 8 dimes and 2 quarters, he would have onefourth as many quarters as dimes and he would have $1.30. 
Problem of the Week #16

SOLUTION
There could be 35 triangles formed in a regular pentagon. 
Problem of the Week #15

SOLUTION
If a 12inch ruler has a mark every eighth of an inch, but not one at 0 or 12, then the ruler would have 95 marks. 
Problem of the Week #14

SOLUTION
It would take a total of 192 secs or 3 mins and 12 seconds to write the numbers 1100. 19= 9 seconds 1099= 180 seconds 100= 3 seconds 
Problem of the Week #13
Build a Staircase This stairway is made of cubes. How many cubes would be needed to make the steps 9 steps high? Show your work using pictures, numbers or symbols. Prefer to work it out by hand? Download a copy of the POW here. 
SOLUTION
You would need 45 cubes to make the staircase 9 cubes high. 
Problem of the Week #12
Halfway Day Collection Pierce students collected half dollars in honor of halfway day to be donated to the Brookline Community Mental Health Center. When the money was sorted there were: Column A Column B 3 tendollar bills 547 quarters 3 fivedollar bills 96 dimes 77 onedollar bills 52 nickels 26 halfdollar coins 238 pennies 3 onedollar coins A. For grades K2: What was the total amount of dollars collected? (Using the information in Column A.) B. For grades 36: What is the total amount of money collected? Show your work using pictures, numbers or symbols. Prefer to work it out by hand? Download a copy here. 
SOLUTION
Part A: The total number of dollars collected is $138.00 Part B: The total amount of money collected is $289.33 
Problem of the Week #11
Too Much Valentine's Candy! Three children got on the scale at the same time. They weighed 181 pounds. Then one child got off and the scale read 119 pounds. Then another one got off and the scale read 74 pounds. When the last child got off, the scale returned to zero. “I weigh the least, because I am the smallest,” said Sophie. “I weigh the most because I am the biggest,” said Morgan. “I must have eaten too much Valentine's candy,” said Danny. How much does Sophie weigh? Show your work using pictures, numbers or symbols. Prefer to work it out on paper? Download a copy here. 
SOLUTION
Sophie weighs 45 pounds 
Problem of the Week #10
Sum of Digits is 24 985 (9+8+5=22) The sum of the digits in the number 994 is also 22 (9+9+4=22). How many 3digit even numbers are there that have 24 as the sum of their digits? Record all the possibilities. Show your work using pictures, numbers or symbols. Rather work it out by hand? Download a paper copy here. 
SOLUTION
There are FOUR 3digit even numbers with a sum of 24: 888,996,978, and 798 
Problem of the Week # 9

SOLUTIONThere are 132 dates in each year that could be unclear (For each of the 12 months, there are 11 dates that could be reversed, and 12 x 11=132).

POW #8
The Sporting Store
The sporting Store bought baseballs and softballs. The owner realized that 3 baseballs cost the same as 4 softballs. It costs $14.00 to buy one baseball and one softball.
How much does 1 baseball cost? Prefer to work on paper? Download a copy here. 
SOLUTIONOne baseball would cost $8.00 (Given the information that 3 baseballs cost the same as 4 softballs, and it costs $14 to buy one of each, then 3 x $8.00 = 4 x $6.00 and $8.00 + $6.00 = $14.00)

Problem of the Week #7

SOLUTIONQuestion 1: Answer is 1/4.
Question 2: Answer is $600 (the striped and checkered sections make up 9/16 or 3/4 of the window, 3/4 of $800 is $600). 
Problem of the Week #6

SOLUTIONA=7
B=8 C=9 D=5 E=4 F=3 
Problem of the Week #5

SOLUTION
Question A: 30 families (If each family donated $50, then you would need 30 families to reach $1500.)
Question B: $200. (If 50% of the approximately 500 families at Pierce wanted to raise $50,000, each family would need to contribute $200.) 
Problem of the Week #4

SOLUTION
The solution to problem #4 "Halloween Costumes" is 5 trickortreater are wearing neither a mask nor a hat. 
20122013 Solution Archive
20112012 POW ARCHIVE
Problem of the Week #12

SOLUTIONIf there are 16 basketball teams in four regions and each team plays until they lose one game, then the answer is that there are 63 games in the tournament.

PROBLEM OF THE WEEK #6

SOLUTIONThe correct answer to "Unicef Collection" is as follows: The total bills and checks for questions A is $441.24 and the total bills, checks, and
coins for question B is $1,268.87. 
PROBLEM OF THE WEEK #3

SOLUTION
The correct answer was either 30 or 32 minutes.

PROBLEM OF THE WEEK #2

SOLUTION
The correct answer was Jack had 55 shells.

PROBLEM OF THE WEEK #1

SOLUTION
The correct answer was that 7 cats ate mousie meat (2 lucky cats ate 7 mice each and 5 unlucky cats ate 2 mice each, for a total of 24 mice).
