By TengCHBy TengCH

The Most Beautiful Mathematical

Magic Games & Puzzles (01)

宽柔

16 of The Most Beautiful Mathematical Magic, Games & Puzzles

(01)1. The Flash Mind Reader Crystal ball magic2. Sum of 10 numbers Fibonacci Magic3. 3-digit numbers, abc Magic Number 94. Five Tetrominoes $10K Puzzle 5 x 4 rectangle5. Magic Tables Binary Magic6. Secret of Dies7. Traffic Jam Leap frogs Best Team-building

game8. Tower of Hanoi （河内之塔） Mathematical Recurrency9. Sum to 20 Game strategy 3 levels.10. Bai Qian Mai Bai Ji 百钱买百鸡） Problem of the 100

Fowls11. Han Xin Dian Bin （韩信点兵 ) Remainder Theorem12. 9 Flips13. Consecutive Sum14. The Singapore Polytechnic Lockers 15. Winners & the Chocolates16. $5 & $2 notes17. Who keep the Fish? ( 谁家养鱼 ?) & More

•Think of a two digit number

•Add both digits together

•Subtract the total from your original.

•Look up on the chart for your final number.

•Find the relevant symbol.

•Click on the crystal ball.

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Get two participants as VolunteersEach of them suggests a number, any

number between 1 to 20.

The third number is the sum of the first two numbers, the forth number will be the sum of second & third number, so on and so forth,

The subsequence number will be the sum of the previous two numbers, until you have all the 10 numbers

Now, ask the volunteers to add up all the 10 numbers.

( Someone will be able to tell you the SUM well before they have completed the calculation. Why?)

2 Sum of 10 numbers Fibonacci

Magic

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Think of any three digit number ABCRearrange the same three digits in any

order to form another number, eg. BAC

Work out the difference of the 2 numbers. You get xyz or xy

Remove one of the digit (except 0)from your answer, and show me the remaining digits. I will be able to tell the digit that you had removed.

Why? How?Three different digits

http://trunks.secondfoundation.org/files/psychic.swf

3 Magic Number 9

Cast out 9, Divisible by 9

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4. The Five TetrominoesThe Five Tetrominoes

magic/puzzleTrace the five

shapes shown in the Figure on a sheet of cardboard or stiff paper, and cut them out.

Can you fit them together to make the 4 x 5 rectangle as shown in ?

Pieces may be turned

over and placed with either side up.

Using the 5 Using the 5 different different shapes shapes of tetrominoes.of tetrominoes.

Can you fit them together to Can you fit them together to form a form a 4 x 5 4 x 5 rectanglerectangle as shown? as shown?

Pieces may be Pieces may be turned over and turned over and placed with either placed with either side up.side up.

You will be rewarded with You will be rewarded with $10K if you form it within $10K if you form it within one hour one hour

1 3 5 7

9 11 13 15

17 19 21 23

25 27 29 31

Table A

2 3 6 7

10 11 14 15

18 19 22 23

26 27 30 31

Table B

4 5 6 7

12 13 14 15

20 21 22 23

28 29 30 31

Table C

8 9 10 11

12 13 14 15

24 25 26 27

28 29 30 31

Table D

16 17 18 19

20 21 22 23

24 25 26 27

28 29 30 31

Table E

5. Magic Tables

7. Traffic Jam - Fishing Boat Leap-Frog

Ten Men are fishing from a boat, five in the front, five in the back, and there is one empty seat in the middle. The five in front are catching all the fish, so the five at the back want to change seats.

To avoid capsizing the boat, they agree to do so using the following rules:

1. A man may move from his seat to and empty seat next to him.

2. A man may step over only one man to an empty seat.

3. No other move are allowed.What is the minimum number of moves

necessary for the men to switch places?If there are n men from each side, how

many moves is needed for the swap?

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8. Tower of Hanoi 河内之塔

http://www.mathsnet.net/puzzles/hanoi/

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8. The Tower of Hanoi 河内之塔 The French mathematician Edward Lucas (1842-

1891) constructed a puzzle with three pegs and seven rings of different sizes that could slide onto the pegs.

Starting with all the rings in one peg in order by size, the problem is to transfer the pile to another peg subject to two conditions:

Rings are moved one by one, and no ring is ever placed on top of a smaller ring.

Legend has it that an order of monks had a similar puzzle with 64 large golden disks.

The monks supposedly believed that the world would crumble when the job was finished.

How many moves are required? For n rings?

http://www.mathsnet.net/puzzles/hanoi/

Select all the cards with 1 to 5You are now having a pool of cards with

4 sets of cards from 1 to 5, all cards are open, facing up.

Play between 2 players (0r 2 teams of players)

The players take turns to choose a card from the pool, and sum up the numbers of all the cards selected from both players

Whoever gets the last card that the total sum reaches 20 win the game.

Who will win? How?

9.

A man paid exactly 100 dollars for 100 chicken

A rooster cost $5 each, a hen cost $3 each, and a dollar for 3 chicks

How many roosters, hens and chicks did the man buy?

百钱买百鸡

10 Bai Qian Mai Bai Ji

（韩信点兵） 11 Han Xin Dian Bing 1/2

1. 韩信 Han Xin, an Han dynasty general, devised a method to count the exact number of his soldiers.

2. He arranged them in rows of 5, 6, 7 and 11, from the remainders, he will be able to know the exact number of his soldiers.

3. How did he do that?

4. With the respective remainders of 1,5, 4,10, What is the exact number of 韩信’ s soldiers?

Han Xin Dian Bing Solution

韩信点兵 Simplification Methods

Two Remainder Theorems: 余数定理1.Number X multiply by M, remainder also multiply by M2.Addition of Multiple of divisor, X + D x M, Remainder unchanged

NoDivisor

DRemainder X Remainder Multiplication

of remainder

value

N 3 2 5x7=35 2 1 35

N 5 3 3x7=21 1 3 63

N 7 2 3x5=15 1 2 30

Sum 128

LCM 3x5x7 105

Final Answer N= 23

Han Xin Dian Bing SolutionTwo Remainder Theorems: 余数定理

1.Number X multiply by M, remainder also multiply by M2.Addition of Multiple of divisor, X + D x M, Remainder unchanged

韩信点兵 Han Xin Dian Bing; the real question

NumberDivisor remainder X remainder Multiplication

of remainderFinal value

N 5 1

N 6 5N 7 4

N 11 10Sum

LCM

N=

abcdefghijklX 9 lkjihgfedcba

12. 9 Flips

What is the 12 digit number abcdefghijkl ?

Suppose that N is a positive number written base 10, and that 9xN has the same digits as N but in a reversed order. Then we shall say for short that N is a 9-Flip

Find all 9-flips with 12 digitsIs it possible to say exactly how many 9-flips there are with precisely n digits?

13. Consecutive Sums

Some numbers can be expressed as the sum of a string of consecutive positive numbers,

Exactly which numbers have this property?

For example, observe that;5=2+39=2+3+4 =4+511=5+618=3+4+5+6 =5+6+7

What are the consecutive numbers that sum to 30? 30= ?

How about 105? 315? 2310 = ??

13. Consecutive SumsSome numbers can be expressed as the sum of

a string of consecutive positive numbers,Exactly which numbers have this property?

1. What are the numbers have no consecutive sum? Old or even integers? average

2. Exactly How many solutions will it be? If there are more than one solution.

3. How to determine the number of solutions? The Methodology?

4. Fn= ?5. 1=, 2= 3=, 4=, 5=, 6=, 7=, 8=, 9=,10=,…6. The single solution problem.

For example, observe that;5=2+3 9=2+3+4 =4+5 11=5+6 18=3+4+5+6 =5+6+7

What are the consecutive numbers that sum to 30? 30= ?

How about 105? 315? 2310 = ??

At Singapore Polytechnic, there were 1,000 students and 1,000 lockers (numbered 1-1000).

At the beginning of our story, all the lockers were closed.

The first student come by and opens every locker. Following the first students, the second student goes along

and closes every second locker.

The third student changes the state, ( if the locker is open, he closes it; if the locker is closed, he opens it) of every third locker.

The fourth student changes the state of every fourth locker, and so forth.

Finally, the thousandth student changes the state of the thousandth locker.

When the last student changes the state of the last locker,

Which lockers are open?

14. The Singapore Polytechnic Lockers

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15. Winners & the Chocolates (2/3)

After a mathematics quiz, Mrs Lai YM gave the three prize winners a box of chocolate Bars to share.

The first winner received 2/3 of the chocolate Bars plus 1/3 of a bar.The second winner received 2/3 of the remainder plus 1/3 of a bar,The Third winner received 2/3 of the New remainder plus 1/3 of a bar.

And there will no chocolate Bars left after this.

How many chocolate Bars were there in all?How about if there was One bar Left?How about if there were 5 winners?

16. $5 & $ 2 notes

The number of $5 notes to $2 notes is in the ratio 3 : 2 .

When $50 worth of $2 notes are converted to $5 notes, the new ration is 8 : 5.

How many $5 notes are there?

PSLE question

Albert Einstein once posed a brain teaser that he predicted only 2% of the world population would get.

FACTS1. There are 5 houses in 5 different colours

2. In each house lives a man with a different nationality

3. These 5 owners drink a certain beverage, smoke a certain brand of cigarette and keep a certain pet

4. No owners have the same pet, brand of cigarette or drink

17 Who keep the Fish?

谁家养鱼 ?

CLUES1. The Brit lives in a red house2. The Swede keeps a dog3. The Dane drinks tea4. The green house is on the left of the white

house5. The green house owner drinks coffee6. The person who smokes Pall Mall keep birds7. The owner of the yellow house smokes

Dunhill8. The man living in the house right in the

center drinks milk

17 Who keep the Fish?谁家养鱼 ?

9. The Norwegian live in the first house10. The man who smokes Blend lives next to

the one who keeps cats11. The man who keeps horses lives next to

the man who smoke Dunhill12. The owner who smokes Blue Master

drinks beer13. The German smokes Prince 14. The Norwegian lives next to the blue

ouse15. The man who smokes Blend has a

neighbour who drinks waterThe question is, who keeps the fish?

This is not a trick question- it is a genuine logic puzzle.....

17. Who keep the Fish? 谁家养鱼 ?

Rearrange the numbers, such that

Sum of the 8 numbers in the larger circle

Could be divisible by

The product of the 3 numbers in the smaller circle

How?What is your approach?

18. 1 -9 Magic Number

During the Foon Yew Maths Society gathering @ the auditorium

All members will shake hands with each and everyone.

If, there were all together 36 hand- shakes,

How many members are there?

36 Hand-Shakes

20. The Handshaking party

（握手言欢）• On one Saturday, At the Foon Yew High Alumni gathering @ City Square, only five married couples turn out (never happened, fictitious)

• No person shakes hands with his or her spouse. • Of the nine people other than the host, Tan CH,

no two shake hands with the same number of people.

• With how many people does Mrs. Tan, the hostess shake hands?

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21.Ages of my Three Children

Two friends, Chia How and Chong Heng, met at a Foon Yew High gathering @ CITY Sqaure on Sat, after not having seen each other for many years.

As they talk,Chia How asked, ”How many children do you have and what are their ages?”

“I have three children, the product of their ages is 36, and the sum of their ages is your house number.” answered Chong Heng.

Chia How thought for a moment and then said, “I need more information to solve the problem.”

“Oh yes,” replied Chong Heng.”My oldest child is a girl.”

With this additional information, Peter immediately found the answer.

How did Chia How figure out the ages of the children, and what were their ages?

3 Mathematics Tutors are seated one behind another.

Another person showed them 3 grey hats and 2 white hats, blindfolded them, put one hat on each head, and threw the rest away. When the blindfolds were off, they all looked in front of them.

Each was asked in turn what colour hat she or he had. No one could answer. After a long thoughtful silence, the person in front who could see no one’s hat was able to respond correctly about his own hat.

How was this done ?

22. Mathematicians

23. Crossing the Desert

A man has to deliver a message across a desert. Crossing the desert takes 9 days. One man can only carry enough food to last him twelve days.

No food is available where the message must be delivered, but food can be buried on the way out and used on the way back.

There are two men ready to set out together.

Can the message be delivered and both men return to where they started without going short of food?

a b c d e-- f g h i j 3 3 3 3 3

24. 0 -9 Magic Number

‘abcde’ is a five digit number & ‘fghij’ is either a 5 digit or a 4 digit number

The Alphabets a,b,c,d,e,f,g,h,i j represent distinct positive integers from 0 - 9

Find the two numbers What are a,b,c,d,e,f,g,h,I,j represent??

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