4C’s Problem of the Week Solutions
After we discuss our strategies for solving the problem of the week in class, we will add
our solution(s) here.
POW 1
Problem
I am a 5 digit number. My ones digit is 6 more than my tens digit. My tens digit is 3 less
than my thousands digit. My hundreds digit is 3. My ten-thousands digit is 3 times my tens
digit.
What number(s) could I be? __ __ __ __ __
Solutions
● Note that my tens digit cannot be 0, since that would make my ten-thousands digit
0, in which case I am no longer a 5 digit number.
● Since my ones digit is 6 more than my tens digit, my ones digit could be 6, 7 or 9,
corresponding to a tens digit of 1, 2 or 3, respectively.
● My thousands digit is 3 more than my tens digit, so it could be 4, 5 or 6.
● Lastly, my ten-thousands digit, which is 3 times my tens digit, could be 3, 6 or 9.
Therefore I can be 34 317 or 65 328 or96 339
POW 2
Problem
In the old days there were elevator operators to transport passengers. Don Downs always
started his day in the basement. He went up 20 floors to take his boss some coffee.
Then he went down 8 floors to take a muffin to his friend. After that he went up 7 floors to
check his mail. This was the halfway point in the building. How many floors are in this
building?
Solution
We discussed appropriate strategies - drawing a diagram or using addition and
subtraction. We agreed that the basement would equal zero so...
(0 + 20 - 8 + 7) X 2 = 38
There are 38 floors in the building.
POW 3
Problem
Mei Li wants to get the game app, “Angry Nerds” for her old myPhone. She is very frugal
with her allowance money, so she wants to pay the least amount per level.
a) Which of the following versions should she buy?
Version
Ultralight
Costs
$1.00
Levels
2
Light
$2.00
5
Complete
$3.00
8
Professional
$4.00
11
b) If the Complete version is on sale for $0.12 less, does your answer to part a change?
Explain.
Solution
We can determine the amount she would pay per level by dividing the total cost of the
version of “Angry Nerds” by the number of levels in the version. The chart below shows the
cost per level for each version.
Version
Cost
Levels
Cost per Level
Ultralight
$1.00
2
$0.50
Light
$2.00
5
$0.40
Complete
$3.00
8
$0.38
Professional
$4.00
11
$0.36
Thus, in order to pay the least amount per level, Mei Li should buy the Professional
version.
b) If the Complete version goes on sale for $0.12 less, the total cost would be $2.28 and
the cost per level would be $0.36. Since the Complete version and the Professional
version would then have the same price per level, Mei Li must decide whether she is
happy with 8 levels or want to spend $4.00 for 11 levels.
POW 4
Problem
John walks 5 blocks north, 1 block east, and 3 more blocks north. then he walks 1 block
west and 1 block south. How far away is John from where he started?
Solution
John is 7 blocks from where he started.
POW 5
Problem
Brandon, Lauren, Kylie, Robert, and Ashley went trick or treating together. They each wore
a different costume (a ghost, a pirate, Spiderman, a witch, and a goblin).
At the end of the day, each of them counted the number of pieces of candy they collected.
They each collected a different amount of candy (63, 77, 83, 54, and 84).
Figure out the costume worn by each person and the amount of candy each person
collected.
1 Brandon was not a pirate.
2 The boys (Robert and Brandon) costumes included a pirate and Spiderman.
3 Lauren and Kylie collected a total of 161 pieces of candy.
4 The ghost collected 77 pieces of candy.
5 The pirate collected 83 pieces of candy.
6 Ashley and Lauren collected a total of 140 pieces of candy.
7 The witch collected the most pieces of candy.
Solution
We used the matrix below to solve the problem, filling in the information given to us and
eliminating possibilities.
POW 6
Problem
There are four students in the class. Carter is 15 kilograms lighter than Sally. Gary is twice
as heavy as Carter. Jeremy is seven kilograms heavier than Gary. Jeremy weighs 71
kilograms.
What is SAlly’s weight?
Solution
By working backward we can solve this problem. Jeremy is 7 kg heavier than Gary, so if
we subtract 7 kilograms from Jeremy’s weight, we will know Gary’s weight (71 - 7 = 64).
Gary weighs 64 kg. Gary is two times heavier than Carter, so if we divide Gary’s weight by
2, we will know Carter’s weight (64 / 2 = 32). Carter weighs 32 kg. Carter is 15 kg lighter
than Adrian, so if we add 15 kilograms to Carter’s weight, we will know Adrian’s weight (32
+ 15 = 47). Adrian weighs 47 kg.
POW 7
Problem
Stripes, a baby tiger, was born at the zoo on November 25th weighing 2 kg. He had a
healthy appetite and at the end of the first week Stripes weighed 4 kg. The zoo’s vet came
to weigh the tiger cub again at the end of the second week and was shocked to see that
he had grown to weigh 6kg.
If this growing rate continues, how much will Stripes weigh when he is two months old?
Solution
By looking for a pattern we are able to solve the problem.
We see that each week Stripes is 2 kg heavier and so in the third week he weighs 8 kg (6
+ 2). We need to continue the pattern until we get to 8 weeks (equivalent to 2 months).
Stripes weighed 16 kg when he was 2 months old.
POW 8
Problem
Four children each caught a fish while at the beach. Teri's was double the size of Jane's.
Jane's fish was shorter than Lynn's by nine centimetres. Lynn's was 18 centimetres longer
than Roger's, who caught a fish 30 centimetres long. How long was Teri's fish?
Solution
Working backwards we find...
Roger’s fish = 30 cm
Lynn’s fish = 30 + 18 = 48 cm
Jane’s fish = 48 – 9 = 39 cm
Teri’s fish = 39 x 2 = 78 cm
POW 9
Problem
Ole Santa's pack held thirty toys
Made by his elfin crew;
And though none made the same amount,
Each elf made more than two.
The elf named Cher made one more toy
Than the elf who dressed in reds,
But Cher made one less Christmas toy
Than the elf who made the sleds.
Spry Johnny elf made racing cars;
Five toys were made by Jane.
The elf who dressed in yellow suits
Made each and every train.
The elf who always dressed in green
Made one-third as many as Sue.
Cute Marcia elf was dressed in orange,
And one elf dressed in blue.
The elf who made the spinning tops
Made the most toys of them all.
Another perky, smiling elf
Made each and every ball.
Ole Santa's pack held 30 gifts
All tagged for girls and boys.
From the clues that you've been given,
Now guess who made what toys.
Solution
Each elf made at least three toys (line 4). One elf made three times as many as another
(13-14), and three elves made consecutive amounts (5-8). If you eliminate duplicate
amounts (3), two possible number combinations total 30: 12/6/5/4/3 or 9/7/6/5/3.
With either solution, Sue made the most (13-14). And we know that she made tops 17-18).
She was not dressed in green (13-14), orange (15), red (5-6), or yellow (11-12), so she
must be the elf in blue.
The two elves who made the least must be dressed in green (13-14) and red (5-6).
Therefore the elf who made the least can not be Marcia (15). It also can not be Cher (5-8),
or Jane (10), so Johnny must have made the least. And he made cars (9).
The elf who made the second most was not Jane (10)or Cher (5-8), so it must have been
Marcia.And Marcia dressed in orange (15).
Since the two elves who made the least were in green and red, the elf in yellow must have
made the third-smallest amount of toys. And that elf made trains (11-12).
Since the elf making sleds could not have made the second-smallest amount of toys (7-8),
Marcia must have made the sleds. Cher is therefore the elf in yellow, and the person who
made the second-smallest amount of toys is in red (5-8).
By elimination, Johnny is in green, and Jane is in red and made the balls. Since the elf in
green made three toys, Sue must have made nine toys (13-14), and our amounts of toys
must be: 9/7/6/5/3.
Sue (blue) made 9 tops.
Marcia (orange) made 7 sleds.
Cher (yellow) made 6 trains.
Jane (red) made 5 balls.
Johnny (green) made 3 cars.
POW 10
Same as POW 8