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Problems 101 to 150
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Gabriel buys 182
tiles that measure one meter on each side. He places the tiles in a rectangle
almost square.
Find the measurements of the rectangle in whole values.
Draw six straight
lines to form two squares of the same size.
In this figure, draw five squares of
the same size without tracing straight lines horizontally or vertically.
Find a number that
is a square and that remains a square if we add or subtract 120 from it.
Find the number of
squares in this sequence : 1, 3, 5, 7, 9, 11, 13, …, 299.
Kate rented an
apartment on the 45^{th} floor of a building of 85 floors on November 1^{st}
2008. She wanted to move twice a year : up five floors on March 1^{st}
and down three floors on November 1^{st}.
On which floor, will Kate live
on April 1^{st} 2013 ?
On a rectangular
board, Larry throws 84 darts. At the end, each line contains 28 darts and each
column 21. The empty squares have respectively from 1 to 9 darts, except 7.
Indicate the number of darts per
empty square.
What can be done
with one 4 and one 5 ? Find at least four possibilities.
Each of the digits is represented below
with some clubs.
0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
§§§ 
§§ 
§§§ 
§ 
§§§§ 
§§§ 
§ 
§§§§ 
§§§ 
§§ 
What is the greatest number of
three different digits that uses 10 clubs ?
Using four 3,
represent successively 7, 8, 9, 10, 11 and 12. The allowed operations are : +,
–, ´ and ¸, as well
as the square root.
Each letter represents a different
digit. For example, R = 2 and P = 4. The sum of numbers in each line, column and
diagonal is equal to PB.
RR 
B 
SB 
SR 
SM 
RN 
SP 
RP 
SN 
What is the value of PB ?
In the empty squares, write each of the
numbers from 1 to 8 so that you obtain the horizontal and vertical results.
8 
´ 

+ 

= 
20 
´ 

´ 

+ 



+ 

 

= 
9 
 

+ 

+ 



 

´ 

= 
18 
= 

= 

= 


16 

19 

11 


I am the smallest
number that is divisible by the numbers from 1 to 9. Who am I ?
Bill has a
rectangular ground. Its length is higher of 25 meters than the width. Bill
wishes to divide its ground into 15 parts each one measuring 60 square meters.
What is the length of the ground ?
This figure consists of eight balls and
five rows of three balls each one.
Using nine
balls, form four rows of
three balls each one.
In my
school, there is a mathematics club. Its phone number
is ABCDEFG.
A is half of B.
B is smaller than C by one.
C added to D is an odd
number.
D is half the sum of A and B.
E is C minus A.
F is C minus B.
G is the sum of A and B minus C.
What is the phone number of the club ?
Nine buses carry 234
passengers. At a
particular moment, the nine buses have the same number of passengers in each
horizontal, vertical and diagonal row. Moreover, the buses B and G have 39 and
31 passengers respectively.
A B C
v v
v
D E F
v v
v
G H I
v v
v

What is the number of passengers on
the other buses ?
Among the following
expressions, which is the greatest : 8^{9} or 9^{8} ?
You take the number 40. You make these
operations in various orders : to add 5, to subtract 5, to multiply by 5 and to
divide by 5.
Find the smallest
result.
In the board, each letter corresponds
to a different digit. For example, M = 3 and G = 7. The sum of the numbers of
each line is given on the right and that of each column at the bottom. When two
letters are joined, they form a twodigit number.
M 
P 
D 
HA 
J 
G 
M 
HJ 
H 
P 
B 
HP 
P 
EM 
HG 
JP 
What is the value of
JP ?
A pawn moves diagonally on a
rectangular board. It begins at point A and stops on the last row.
How many paths can it make ?
Marilyn decided to write the digits
with balls.
What is the greatest
odd number of two different digits that requires 10 balls ?
In this figure, Zachary wants to place
each number from 3 to 11. He wrote the 5 and the 8.
Write the other
numbers. The sum of
the numbers of the cells joined by a straight line must be equal to 21.
Examine carefully the numbers in the
first three circles.
Complete the fourth
circle.
A clothing store paid this advertising
space in a newspaper. The cost of three articles is mentioned.
Pants
45 € 
Socks 
Jacket
41 € 
Swinsuit

Shoes 
Coat 
Shirt
31 € 
Boots 
Waistcoat 
Find the cost of the other articles, since the total cost is of 108 euros in
each horizontal, vertical and diagonal row.
Place signs + between some digits of
this number. The sum must be 121.
Represent 100 by
successively using six 8, seven 8, eight 8, nine 8, ten 8, eleven 8 and twelve
8. The allowed operations are : +, –, ´ and
¸.
Raymond divided his field in 30 square
pieces. He planted six trees, one by piece.
Determine the number of grounds 2 ´ 2 that have only
one tree.
Gerry has a bag of
balls. He sells a third of his bag and gives three balls. Again, he sells a
third of the remaining balls and gives three balls. For the last time, he sells
a third of the remaining balls and gives three balls. He has then seven balls in
his bag.
How many balls had Gerry at the beginning ?
In the grid, place numbers so that the
sum in each line and in each column is 50.
12 
17 
2 

12 
16 
6 

11 



10 

15 

9 

14 

8 

18 
3 
8 
Marilyn decided to write the digits
with balls.
Find the smallest
even number of two digits that requires 11 balls.
Henry chooses a
twodigit number. He multiplies by 3, adds 12, divides by 3 and subtracts the
chosen number. What is the result compared to the chosen number ?
Find the 15^{th}
number of this sequence : 2, 5, 4, 7, 6, 9, 8, 11, ...
Martin bought 99
flowers. He wants to
arrange them in six blocks. The three blocks of corners must contain 10, 12 and
17 flowers. The number of flowers must be the same in each row of three blocks.
How many flowers did Martin plant
in each block ?
In the diagram, there are six squares
and 17 matches.
Remove six matches
and obtain two rectangles.
Find two numbers the
sum of squares of which is 274.
Peggy wants make a square carpet with
25 squares of same size. She has five red squares, five blue, five purple, five
yellow and five grey. Eight squares have already their color.
Arrange the colors so that each one appears once in each horizontal, vertical
and diagonal row.
Passing by the points
of this figure, form six lozenges of same size.
In a box, Ann placed 15
tokens.
· 5 tokens marked 1 point
· 5 tokens marked 2 points
· 5 tokens marked 5 points
Remy wants nine tokens with a total of 17 points. What tokens
will Remy receive ?
Cynthia owns four apartment buildings.
The number on each one is composed of the same four digits whose the sum is 20.
The sum of the four numbers is 22 220.
Find the numbers.
Four times the sum
of a twodigit number is equal to this number. Twice the product of the two
digits is also equal to this number. What is this number ?
In the addition, each letter represents
a different digit. For example, R = 2 and M = 8.
M A T H
+ M A T H
P O W E R

What is the value of
POWER ?
Pascal traces a
continuous line from a point of the circumference to another. Thus he divides
the circle in five parts.
Trace two other
straight lines continuously for having a maximum of parts. What is this maximum
?
Among the six
numbers, there is only
one that is not a square.
414 736 
477 481 
606 841 
547 602 
558 009 
795 664 
Find this number without extracting any square root.
This figure consists of eight balls and
five rows of three balls each one.
Using seven
balls,
form four rows of three balls each one.
Each letter represents a different
digit. For example, R = 8.
What is the value of
RITE ?
The divisors of 16
are 1, 2, 4, 8 and 16. The sum of these divisors is 31. Find another number
where the sum of the divisors is also 31.
In the four
operations, each letter represents a different digit.
Quelle est la valeur de FKMP ?
In a village, a new number system was
adopted. There are only two digits, 0 and 1. The table of equivalence is as
follows :
0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
0 
1 
10 
11 
100 
101 
110 
111 
1000 
1001 
1010 
There are 11 ´ 111 ´
1111 inhabitants in this village. What is that number in our system ?
In this series of
six dominos, the upper row contains 20 points and the bottom row 12 points.
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Move two dominos in order to obtain the same number of points
per row.
