Prime Factor Math Circle 3-4. Session 15. Math Domino Answers.
Problem
Cut this ring into 4 pieces with 2 straight
through-cuts. (Do not draw on this card – copy
the picture first.)
Answer
(Note that other answers are possible)
Cut this ring into 3 pieces with 2 straight
through-cuts. (Do not draw on this card – copy
the picture first.)
(Note that other answers are possible)
1
2
Cut this ring into 5 pieces with 2 straight
through-cuts. (Do not draw on this card – copy
the picture first.)
3
4
Cut this shape into 6 pieces
with 2 straight throughcuts. (Do not draw on this
card – copy the picture
first.)
5
6
The two triangles sketched on the picture
below overlap. Their comon part has a shape
of a triangle (colored grey).
Now, here is my the question: can you draw
such a pair of overlapping triangles that their
common part is a rectangle?
The two triangles sketched on the picture
below overlap. Their comon part has a shape
of a triangle (colored grey).
Now, here is my the question: can you draw
such a pair of overlapping triangles that their
common part is a rectangle?
Cut the figure into two equal parts (equal in
shape and size). Cut along the gridlines only.
7
Cut the figure into two equal parts (equal in
shape and size). Cut along the gridlines only.
(Do not draw on this card – copy the picture
first.)
8
other answers are possible
Cut the figure into two equal parts (equal in
shape and size). Cut along the gridlines only.
9
Insert several plus and minus signs in such a
way as to get a correct equality.
10
11
12
13
Who is right?
Ben: “ I can write the largest number ever
using only digits nine.”
Emma: “There is no such thing as a largerst
number.”
Rachel: “The largest number that exists ends
with 0.”
Bella wrote down all the numbers from 1 to
45. How many times did she write digit 3?
The Cool Girls team participated in 4 Math
Domino games. It is known that:
- The team solved twice as many problems on
their 2nd Math Domino contest as they did on
the 1st one.
- They solves four problems less on the 3rd
contest than on the 2nd one.
- The team solved three times as many
problems on the 4th contest than they did on
5-4+3-2+1=3
(Several answers are possible)
Emma
4+10= 14
7
the 3rd one.
- They solved 30 problems on the 4th contest.
How many problems did Cool Girls solve on the
1st contest?
14
In a magical kingdom, there live two-headed
dragons and three-headed dragons. There are
three times as many two-headed dragons as
three-headed dragons. Altogether, these
dragons have 27 heads. How many dragons are
there in this kingdom?
15
Benny the Bear Cub weighs more than Lenny
the Lion Cub, and Tommy the Tiger Cub weighs
less than Charley the Chimpanzee Cub. Charley
is not the heaviest of all four animals. Can you
tell who is the heaviest?
16
Benny the Bear Cub weighs more than Lenny
the Lion Cub, and Tommy the Tiger Cub
weighs less than Charley the Chimpanzee Cub.
Can you tell who is the lightest of the four
animals? Either explain who is the lightest, or
come up with an example showing that it is
not possible to determine who is the lightest.
17
The window is made of 8 square panels. The 2
big square panels in the center are of the same
size, and the 6 small square panels on the
sides are all of the same size. The sidelength of
each big panel is 3 feet. What are the length
and the width of the window?
12 dragons
Benny is the heaviest
Either Lenny of Tommy is the lightest. Examples:
Benny weighs 150, Lenny 20, Charlie 100, and
Tommy 80.
Benny weighs 150, Lenny 140, Charlie 100, and
Tommy 80.
Height: 6 feet, width 7 feet
Sruttika penciled a number in each circle. Next,
she connected some of the circles with arrows
in such a way that an arrow always points in
the direction of a smaller number. Sanghavi
erased the numbers.
Restore the missing numbers if you know that
these numbers are 5, 6, 7, 8, 9.
18
?
9
8
?
?
7
6
5
?
?
Miles penciled in a number in each circle. Next,
he connected some of the circles with arrows
in such a way that an arrow always points in
the direction of a smaller number. When Max
came in he erased all but one number.
Restore the missing numbers if you know that
these numbers are 4, 8, 9, 13, 20.
19
?
?
?
20
8
9
?
?
13
20
4
6
6
Below is the picture of a chocolate bar. The bar
is made of two big squares, and of six small
squares. You can choose either the left part of
the bar (made of all small squares) or the right
part of the bar (made of all big squares). Which
one would you choose? (Assume that you
want to choose a bigger part). Explain your
answer (If you just measure the sides with a
ruler – that is not an explanation).
Left. The height Is the same, and the width is
bigger (two small squares are more than one side
of a big square)
21
22
23
Five pencils of five different colors (red, green,
blue, yellow, white) are placed in a row. It is
known that:
- The red pencil is next only to the blue
pescil.
- The blue pencil is between the red and
white pencils.
What color is the pencil in the center?
Vadim rolls three six-sided dice. The dice show
3 different numbers,
and the sum of these
numbers is equal to 7.
How many of Vadim’s
dice show 1?
Chirag, Leonid, Katya and Mila were given a
six-sided die each. Every child rolled his or her
die once, and everyone got a different
number. It is known that:
- Chirag’s number was 4 times greater than
Leonid’s.
- Katya’s number was 3 times greater than
Mila’s.
What number did Mila roll?
White
Answer is 1. (Note: ask for explanation.)
Explanation: if there were no 1, then the sum
would be at least 2+3+4=9.
Answer is 2. (Note: ask for explanation.)
Explanation: Sid got 4, Masaya got 1. There are
two choices for Alex and Filip: 6,2 and 3,1.
However, since all the numbers are different,
then (3,1) is not possible.
24
Mr. Holmes, the 3rd grade teacher, has a party
jar on his table. At the end of each school day,
Mr. Holmes either rewards his class’s for good
behaviour by adding one marble to the jar, or
fines the class by removing one marble.
On Monday morning, the jar contained 12
marbles. In two weeks (after 10 school days)
the jar conained 14 marbles.
How many days did Mr. Holmes reward the
class for good work?
6 days
It is 10 miles from Frogville to Dragonville, 14
miles from Toadville to Scaryville, and 20 miles
from Frogville to Toadville. How far is it from
Dragonville to Scaryviille?
25
FF
Frogville
FF
Dragonville
e
Scaryville
FF
10
Toadville
FF
4 miles
14
20
26
There are 5 diamonds and 14 rubies in a dark
cave. What is the smallest number of stones
you should take (without looking) to make sure
that you have 2 rubies?
27
The candy box contains 6 red jelly beans, 5
yellow and 7 blue jelly beans. What is the
smallest number of candies you should take
(without looking) to make sure that you have 2
beans of the same kind?
7 stones
4 beans
28
There are five flowers in the vase - roses and
carnations.
Out of any two flowers, at least one is a rose.
How many carnations are there in the vase?
29
Harry, Hermione, Ron and Neville were waiting
in line to take the levitation test. While
waiting, Ron traded places with Neville. Next,
Ron traded places with Harry.
Finally, the students took the test in the
following order: Hermione, Neville, Ron, Harry.
What was their order in the beginning?
Answer: 1. (Note that this problem needs an
explanation.)
Hermione, Ron, Harry, Neville.
How many lines of symmetry does this shape
have?
7
30
31
32
Baby Samuel is learning to walk. Each day, he
makes as many steps as he made during the
two previous days together. (For example, if
he made 4 steps yesterday and 6 steps today,
then he’ll walk 10 steps tomorrow.)
Baby Samuel started walking on Monday. On
Thursday, he made 9 steps, and on Friday – 15
steps. How many steps did he make on the
first day (Monday)?
There are three locked chests in the wizards
cave. One of them contains the Stone of
Wisdom, the other ones are empty.
The sign on the first chest reads “The stone is
not here.” The sign on the second chest reads
“The stone is in the third chest.” The sign on
the third chest reads “The stone is in the
second chest.”
If you know that two of these signs are false
3
In the first chest
and one is true, can you tell where the stone
is?
33
34
Prince Ivan is looking for Princess Masha who
was kidnapped by King Haggard. Prince Ivan is
on the crossroads where three narrow roads
start. A wooden sign is posted on each road.
- The first sign reads: “The second road leads
to the princess.”
- The second sign reads: “Follow this road and
you will find your princess.”
- The third sign reads “Princess: this way.”
The wise raven tells the prince that only one
of this signs is true. Help the prince choose
the right road.
Third road
Zarrina needs $4 more to buy 5 ice creams.
However, if she buys 3 ice creams, she will
have $2 left. How much does one ice cream
cost?
$3
How many triangles are there on the picture?
35
10
36
There are four rooms in the basement: family
room (F), office (O), bedroom (BD) and
bathroom (BH).
The family room and the bathroom have
square shapes. The perimeter of the family
room is 24 yards; the perimeter of the office is
20 yard.
What is the perimeter of the bathroom?
F
BD
O
BH
37
How many 4-digit numbers are there such that
the sum of their digits is 3?
38
There are three gnomes living in the valley of
Treasureville: Bella, Max, and Ilya.
- Bella has 42 diamonds in her collection.
- Max has 18 diamonds in his collection.
- Ilya's collection has fewer diamonds than
Bella's by the same number of diamonds that
his collection is larger than Max's.
How many diamonds does Ilya have?
39
16
Insert several arithmetic operation signs (“+”,
“-“, “ ”, “ ”) in such a way as to get a correct
equality. You can use several signs of the same
kind, and you do not have to use all 4 different
signs.
10
30 diamonds
2*2/2/2=1