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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?
Special Number Patterns for whole number
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?
Special Number Patterns for whole number
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?
Special Number Patterns for whole number
How about this number 37037?37037 × 3 =37037 × 6 =37037 × 9 =37037 × 12=37037 × 15 =37037 × 18 =37037 × 21 =37037 × 24 =37037 × 27 =
Special Number Patterns for whole number
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?
Special Number Patterns for whole number
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?
Special Number Patterns for whole number
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
from the above operations?
Special Number Patterns for whole number
e.g. 12 = 11 + 1123 = 111 + 11 + 1Express the followings in the similar
form.1234 = 12345 =123456 =1234567=
Special Number Patterns for whole number
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?
Special Number Patterns for whole number
78 + 23 = 778 + 223 = 7778 + 2223 =77778 + 22223 =
777778 + 222223 = 7777778 + 2222223 = 77777778 + 22222223 =777777778 + 222222223 =What is the special pattern that you observe
from the above operations?
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