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Problems to Ponder over the Summer
1. What is the next member of the sequence 137 106 79 56 37 22 11 ___
2. Among 20 children who either play hockey or football (but not both), 9 play football, 8 are
boys, and 8 girls are hockey players. How many boys play football?
3. A cardboard box measuring 7 x 14 x 5 is filled full with 1 x 1 x 1 sugar cubes. How many of
these 490 sugar cubes touch at least one face of the box?
4. The average of 33 consecutive whole numbers is 58. What is the smallest of these whole
numbers?
5. On this number line, length PR = 14, length QS = 18 and length PS = 24. What is the length of
QR?
P
Q
R
S
6. Here are 4 views of the same block. Draw the correct top on the fourth block.
7. I woke up this morning to find the hour hand pointing directly at the 38 minute mark. What
time did I wake up?
8. Place the numbers 1 through 9 in the boxes to make all arithmetic statements true.
9
9
9
9
9
9
Problems to Ponder over the Summer
9. Groups of campers were going to an island.
On the first day, 10 went over and 2 came back.
On the second day, 12 went over and 3 came back.
If this pattern continues, how many would be on the island at the end of a week?
10. A team of scientists found that there were 4 oak trees for every 10 pine trees. How many
oak trees were there if they counted 36 more pine than oak?
11. All of the letters below could represent the digits 3 to 9. (None can represent a 0, 1, or 2)
Determine what digit each letter represents, to make this sum correct.
one
+ one
two
12. During one month, exactly half of the 180 babies born at Grand River Hospital were boys, and
40 of all babies weighed 4 kg or more. There were 26 baby boys who weighed 4 kg or more.
Complete the table below:
Less than
4 kg
4 kg
or more
Boys
Girls
13. The mean for a set of eight numbers is 12. When another number is added to the set, the
mean changes to 11. What number was added?
14. Asha receives $10 000.
Asha keeps half his money and gives the rest to Bertha.
Bertha keeps half her money and gives the rest to Calvin.
Calvin keeps half his money and gives the rest to Dane.
Dane keeps half his money and gives the rest to Evanna.
Which expression shows the dollar amount of money that Evanna receives from Dane?
a. 10 000 ÷ 2 4
1 1

2 2
1 1 1 1
c. 10 000 ÷
÷
÷
÷
2 2 2 2
b. 5000 
d. 2500 ÷ 2
Problems to Ponder over the Summer
15. The given diagram shows the measures (in degrees) of some of the angles. Find the value of
x.
5x
3x
7x
4x
6x
16. A perfect number is a number which equals the sum of its distinct proper divisors. For
example, 6 is perfect since 6 = 1 + 2 + 3.
What is the next perfect number?
17. A rectangular block with dimensions 4 x 3 x 2 has all of its surfaces painted red. It is then
cut into cubes with each edge 1 unit. How many cubes have exactly one of its faces painted
red?
18. Simplify
1
1
1
1
1
1
1
5
6
19. Once upon a time, an old lady went to sell her vast quantity of eggs at the local market.
When asked how many she had, she replied:
“Son, I can't count past 100 but I know that.
If you divide the number of eggs by 2 there will be one egg left.
If you divide the number of eggs by 3 there will be one egg left.
If you divide the number of eggs by 4 there will be one egg left.
If you divide the number of eggs by 5 there will be one egg left.
If you divide the number of eggs by 6 there will be one egg left.
If you divide the number of eggs by 7 there will be one egg left.
If you divide the number of eggs by 8 there will be one egg left.
If you divide the number of eggs by 9 there will be one egg left.
If you divide the number of eggs by 10 there will be one egg left.
Finally. If you divide the Number of eggs by 11 there will be NO EGGS left!
How many eggs did the old lady have?
20. What prime number(s) divides perfectly into
210  1
?
Problems to Ponder over the Summer
BRAIN BUSTERS
1. In a market, there are two store that sell fruit, A and B.
Store A sells red plums at 4 for $1 and yellow plums at 3 for $1.
Store B sells red plums at 4 for $1 and yellow plums at 6 for $1.
While at the market you bought m red plums and n yellow plums from each store. You spent a
total of $10. How many plums in all did you buy?
2. Cut any square into squares of two different dimensions in such a way that the number of
smaller squares was the same as the number of larger squares.
3. Look at the following dominoes:
Using all of the above 8 dominoes make a 4 by 4 square where each of the rows and columns add
up to the same number.
However, the dominoes must be in the following form:
Problems to Ponder over the Summer
4. Cut the shape into 8 congruent parts.