m11 recreational mathematics

Recreational Mathematics

Recreational mathematics is a kind of activities using mathematics knowledge to create various types of games as recreational activities, based on certain mathematics principles, laws and theorems for amusement purposes.

There are a few types of recreational mathematics such as number patterns and sequences, number operations, magic square, mathematics games, geometric patterns and tessellations, tangram etc.

Recreation is in the eye of the beholder, and not everything here was originally intended as recreational by its authors

Recreational Mathematics also included a mixture of puzzles, silliness, curious/useless math, and quite serious (but not overly technical) math

Mathematical puzzles vary from the simple to deep problems which are still unsolved. The whole history of mathematics is interwoven with mathematical games which have led to the study of many areas of mathematics. Number games, geometrical puzzles, network problems and combinatorial problems are among the best known types of puzzles.

Number patterns & sequences

Triangular numbers1, 3, 6, 10, 15, ……

1 3 6 10

Number patterns & sequences Square numbers1, 4, 9, 16, 25, …..

,......4,3,2,1 2222

1 4 9 16

Number patterns & sequences

Rectangular numbers4, 6, 8, 9, 10, 12, 14, ……- These numbers can be used to

form a diagram of rectangles.

Special Number Patterns for whole number 1 + 9 × 0 = 2 + 9 × 1 = 3 + 9 × 12 = 4 + 9 × 123 = 5 + 9 × 1234 = 6 + 9 × 12345 = 7 + 9 × 123456 = 8 + 9 × 1234567 = 9 + 9 × 12345678 =What do you see from these whole number

operations?

Special Number Patterns for whole number

0 × 9 + 8 =9 × 9 + 7 =98 × 9 + 6 =987 × 9 + 5 =9876 × 9 + 4 =98765 × 9 + 3 =987654 × 9 + 2 =9876543 × 9 + 1 =98765432 × 9 + 0 =What can you infer from the above operations?


12345679 ×9 =12345679 ×18 =12345679 ×27 =12345679 ×36 =12345679 ×45 =12345679 ×54 =12345679 ×63 =12345679 ×72 =12345679 ×81 =What is the special pattern which you can derive

from the above operations?


1 × 3 × 37 =2 × 3 × 37 =3 × 3 × 37 =4 × 3 × 37 =5 × 3 × 37 =6 × 3 × 37 =What is the special pattern which you can

derive from the above operations?

Special Number Patterns for whole number101 × 11 =101 × 22 =101 × 33 =101 × 44 =101 × 55 =101 × 66 =101 × 77 =101 × 88 =101 × 99 =

What is the special pattern which you can derive from the above operations?

Special Number Patterns for whole number15873 × 7 =15873 × 14 =15873 × 21 =15873 × 28 =15873 × 35 =15873 × 42 =15873 × 49 =15873 × 56 =15873 × 63 =

What is the special pattern which you can derive from the above operations?


How about this number 37037?37037 × 3 =37037 × 6 =37037 × 9 =37037 × 12=37037 × 15 =37037 × 18 =37037 × 21 =37037 × 24 =37037 × 27 =


1 × 1 = 11 × 11 = 111 × 111

= 1111 × 1111

= 11111 × 11111

= 111111 × 111111 = 1111111 × 1111111 = 11111111 × 11111111 = 111111111 × 111111111

=What is the special pattern which you can infer from the

operation above?


Consider these numbers,99 × 2 =99 × 3 =99 × 4 =99 × 5 =99 × 6 =99 × 7 =99 × 8 =99 × 9 =What is the special pattern which you can infer

from the operation above?


99 × 11 =99 × 22 =99 × 33 =99 × 44 =99 × 55 =99 × 66 =99 × 77 =99 × 88 =99 × 99 = What is the special pattern that you can observe



e.g. 12 = 11 + 1123 = 111 + 11 + 1Express the followings in the similar

form.1234 = 12345 =123456 =1234567=


1 + 11 = 12 + 111 = 123 + 1111 =

1234 + 11111 = 12345 + 111111 = 123456 + 1111111 = 1234567 + 11111111 =12345678 + 111111111 =What is the special pattern that you observe

from the above addition?


78 + 23 = 778 + 223 = 7778 + 2223 =77778 + 22223 =

777778 + 222223 = 7777778 + 2222223 = 77777778 + 22222223 =777777778 + 222222223 =What is the special pattern that you observe


Special Number Patterns

You can perform 2 different operations on the same numbers which give you the same answer.

54

54

43

43

32

32

21

21

44

33

22

11

Special Number Patterns

What is the special pattern of the answer?What is the sum of

111

101

51

41

41

31

31

21

21

.

.

.

1

?121

61

41

21

Magic Square

1. Can you fill up the 3x3 square with numbers from 1 to 9 without repetition such that the sum of every diagonal, row and ?.

2.what about 4x4 square?3.what about 5x5 square?4.what about 6x6 square?

Magic Square

3x3 square

4x4 square

6 1 8

7 5 3

2 9 4

16 2 3 13

5 11 10 8

9 7 6 12

4 14 15 1

Magic Square

5x5 square

6x6 square

15 2 21 4 23

6 14 17 18 10

25 19 13 7 1

16 8 9 12 20

3 22 5 24 11

36 2 3 4 5 31

7 29 9 10 26 12

13 14 22 21 17 18

19 20 16 15 23 24

25 11 27 28 8 30

6 32 33 34 35 1

Magic Square

FormulasFor a n x n magic

square.The sum for the

magic number = }1{ 22 nn

Guess a Number

1. guess a number2. subtract 1 from that number3. multiply the answer by 24. add the guess number to the

result.5. what is the guess number?

Cryptogram

FORTY TEN+ TEN

SIXTY such that each alphabet represent

a number, what are these number?

Cryptogram

SEND+ MORE MONEY

FOUR ABCD- TWO x 4 T E N DCBA

PuzzleA guest was visiting Mrs. Blake when Mrs. Blakes’s

three children entered. “I’ve never met your children,” said the guest.“The middle child is Bill,” said the oldest child.“I’m Bob,’ said the middle child.“The middle child is Bart,” said the youngest child.“If you want to know who is who,” said Mrs. Blake, “Bill always tells the truth, Bob tells the truth sometimes, and Bart never tells the truth.”

Identify each of the children.

PuzzleThe following details part of a conversation between Mr. Chai

and Mrs. Latifah at a social gathering in Mr. Chai’s house:

Mr. Chai: I have 3 children. The product of their ages is 72 and the sum of their ages is the same as the number of my house. So, how old is each one of them?

(After going out to the front of the house to have a look at the house number…….)

Mrs. Latifah:I still cannot determine your children’s ages.

Mr. Chai: Okay, I will give another small hint. My eldest child likes to eat vanilla chocolate.

Mrs. Latifah: (After reflecting & doing a bit of maths) Ah, now I see the light. (and she then gave the correct ages of the children.)

PuzzleIn the famous Monty Hall problem, there are 3

doors. Behind one door is a Mercedes Benz (the main prize) and behind each of the other two doors is a goat. The player cannot see what is behind the doors. He selects one door as his choice for the prize. Monty (the T.V. show host) then opens one of the other doors and shows a goat behind it. He then gives the player the choice of sticking to his previous door (still closed) or changing to another ( the remaining closed) door. Should the player stick to his original choice or shift to the other door, and if so, why?

Problem solving

Each of the five digits 1, 2, 3, 4 and 5 is used to fill each of the circles ( in the figure below) such that each line of three digits add up to the same sum. How many possible solutions are there? It is possible for the digit in the centre circle to be an even number? Explain your reasoning.

Problem Solving

Each of the nine digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 is used to fill each of the circles ( in the figure below) such that each line of five digits add up to the same sum. How many possible solutions are there? It is possible for the digit in the centre circle to be an even number?

Problem Solving

How will you measure exactly 2 litres of water using 8-litre and 5-litre containers?

Problem Solving

Ali can paint a wall in 2 working days. Siew Mei takes 4 working days to paint the same wall. How many working days would it take to finish the same job if both work (at the same rates as above) together to paint the same wall?

Problem solving

The area of square A is 25 square units.The area of square F is 4 square units.The area of square G is 25 square units.Find the area of square B, square C.

square D, square E and square H. Explain

AB

C

EF

D

G

H

Problem solving

Mr. Lim has a piece of land as shown below. He decided to divide the land equally in shape and size among his four children. Can you help him to divide the land?

Problem solving Encik Ali has a piece of land which are

planted with 12 rambutan trees as shown below. He wishes to divide that land equally among his four children. Can you help him to do so?

CALCULATOR GAMESAddition estimation game1. Choose any two numbers from the

following and cross them out 26, 53, 7, 46, 14, 4, 31, 29, 20, 2, 37, 33, 18,

35

2. Add them together and use the following table to work out how many points you get.Answer 0-19 20-39 40-59 60-79 80-99

Points 1 2 3 4 5

CALCULATOR GAMESSubtraction estimation game1. Choose any two numbers from the following

and cross them out 48, 52, 9, 12, 67, 25, 32, 1, 93, 100, 27, 70,

18, 39, 4, 832. Find the difference between this two numbers

and use the following table to work out how many points you get.

Answer

0-19 20-39 40-59 60-79 80-99

Points 1 2 3 4 5

m11 recreational mathematics

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