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 Publications



This is the third book published by Récréomath.

Mathematical 
Amusements

Par Charles-É. Jean



This edition includes 200 problems and their solution. The French version is published.

 

Problems 1 to 50

Solutions 1 to 50

Problems 51 to 100

Solutions 51 to 100

Problems 101 to 150

Solutions 101 to 150



Solutions 151 to 200

 

***************
Problems 151 to 200
***************

151

In the diagram, there are six squares and 17 matches.

Remove five matches and obtain three squares.

152

How many squares 2 × 2 can you count in this grid ? Each square must contain exactly one circle and two white squares.

 

 

 

 

n

n

 

 

 

 

 

 

 

n

 

 

 

n

 

 

 

n

 

 

 



153

Andrew possesses eight balls numbered from 1 to 8. How many groups of four balls can have a sum of 16 ?

154

The sum of two numbers A and B is 19. If we add the double of A and the triple of B, the result is 50. Which is the value of A and B ?

155

Find the number of squares in this sequence : 3, 7, 11, 15, 19, 23, ..., 999.

156

Place a sign +, –, ´ or ÷ between the digits of this number in order to obtain 7 like result.



157

In each square, we can read a number.

5

7

3

8

2

3

9

2

4

3

2

5

7

4

9

6

4

3

5

3

4

5

6

7

6

Find the number of rectangles 2 ´ 3 where the sum is less than 26.

158

You choose two numbers. You add, subtract, multiply and divide them. At the end, you add these four results. The greatest selected number is 77. 

Find the smallest number except for 1.


159

In this grid, choose four couples of numbers, a couple by line.

14

3

4

17

6

11

12

9

10

7

8

13

2

15

16

5

Invert the numbers of each couple so that the sum is 38 in each column. The sum of the numbers of each line does not change.

160

Draw one 4 and one 3 to form 43. Remove two segments and move another to obtain the smallest possible number.

Find this number.

161

In the five empty squares, write each digit from 3 to 7 so that the sum is 144.

 

1

 

+

2

 
     
   

8

 

1

4

4

 

162

In the grid, find the number of squares 3 ´ 3 that have only one club.

§

§

 

163

In this grid, write some numbers from 1 to 6. The numbers must be different in each line and in each column.

4

 

 

 

 

3

 

3

 

 

5

 

 

 

1

3

 

 

 

 

6

5

 

 

 

5

 

 

3

 

2

 

 

 

 

5

 

164

On December 1, 2008 was one Monday. Mary is born on March 8, 2009. Find the day of the week of the birth of Mary.

 

165

How many squares 3 ´ 3 can you count in a grid 5 × 5 ?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

166

Elizabeth chooses a number. She makes the operations in this order : to add 12, to multiply by 3, to subtract 6 and to divide by 3. The result is 46. 

Find the chosen number.

 

167

Place a sign +, - or ´ between the numbers so that the equality is true.

 

168

Peter has 32 years and Mary 29 years. When Pierre did he have the double of the age of Mary ?


169

Robert buys stamps for an amount of 234 cents. He wants the same number of stamps of six cents and seven cents. Find the number of stamps of each value.

170

In the circles, write each of the numbers from 1 to 6 so that the sum is 13 in each row of three circles.


171

The age of Adam is triple of that of Blondie. The sum of the ages is 56. Which is the age of Blondie ?

172

In the empty squares, write each of the numbers from 1 to 6.

+

   
     

     

Find the smallest sum.

173

How many squares 3 ´ 3 can you count in a grid 5 × 6 ?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


174

Adelia is born Tuesday on February 29, 2000. Which day of the week was on February 29, 2001 ?

175

Marilyn decided to write the digits with balls.

What is the smallest number of two digits that requires 11 balls ?

176

Find the 19th number of this sequence : 1, 3, 5, 4, 6, 8, 7, 9, 11, 10 …

177

How many squares 4 ´ 4 can you count in a grid 8 × 8 ?

178

Draw six straight lines to form four squares of the same size.

179

A twelfth of a brick weighs the quarter of one kilogram. Determine the weight of four bricks.

180

In the six empty squares, write 2, 4, 5, 6, 8 and 9 so that the addition is true.

 

3

   

  +

 

7

 

 

 

 

 

     

7



181

Find the number of squares in this sequence : 3, 6, 9, 12, 15, 18, 21, …, 999.

182

Brooke rented an apartment on the 75e floor of a building of 85 floors on July 1st 2007. She wanted to move twice a year : up five floors on January 1st and down three floors on July 1st

In which year will she remain on the last floor of the building ?


183

Brice is born on April 25. How many days did he live on June 25 of the same year ?

184

In the nine empty squares, write 2, 4, 5, 6, 8 and 9 so that the equalities are true.

´

=

=

+

=



185

In the circles, write each of the numbers from 1 to 6 so that the sum is 16 in each row of three circles.

 

186

You take the number 51. You make these operations in various orders : to add 3, to subtract 3, to multiply by 3, to divide by 3 and to extract the square root.

The result is 15. Give the order of the operations.

187

Place signs + between certain digits of this number in order to obtain 1066 like result.


188

In each square, we can read a number.

5

7

3

8

2

3

9

2

4

3

2

5

7

4

9

6

4

3

5

3

4

5

6

7

6

Find the number of squares 2 ´ 2 where the sum is more than 21.

189

Billy has a bag of balls. He gives three balls. He sells a third of the remaining balls and gives three balls. Again, he sells a third of the remaining balls and gives three balls. He has then 11 balls in his bag. 

How many balls had Billy at the beginning ?


190

Beatrice chooses a number. She makes the operations in this order : to add 3, to multiply by 4, to subtract 12 and to multiply by ½. 

Which is the relationship between the result and the chosen number ?


191

Find the 14th number of this sequence : 4, 3, 7, 6, 13, 12, 25, 24, 49, 48, 97, 96, ...

192

In a box, Brenda placed 15 tokens.

· 5 tokens marked 1 point

· 5 tokens marked 2 points

· 5 tokens marked 5 points

Benjamin wants six tokens with a total of 17 points. What tokens will Benjamin receive ?

 

193

Draw six straight lines to form three triangles of the same size.


194

Which number is the greatest : 98 763 ´ 98 765 or the square of 98 764 ?

195

This figure consists of eight balls and four rows of three balls each one.

Move one ball in order to obtain five rows of three balls each one.

196

In the addition, each letter represents a different digit. For example, A = 8 and P = 4.

     P A R
  + P A S
      S B P

Which is the value of R ?

197

Draw one 8 and one 5 to form 85. Remove three segments to obtain the greatest possible number.

Which is this number ?

198

Using these numbers, represent 109. The allowed operations are : +, –, ´ and ¸.

 

199

Draw six straight lines to form four triangles of the same size.

200

Adele places eight coins in a circular way. She removes a first coin and successively the third coin. She continues thus until a single coin remains.

What coin will be the last ?

 

 

Problems 1 to 50

Solutions 1 to 50

Problems 51 to 100

Solutions 51 to 100

Problems 101 to 150

Solutions 101 to 150



Solutions 151 to 200