Libevents Mathmagic Slides

7/31/2019 Libevents Mathmagic Slides

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By TengCH

The Most Beautiful

Mathematical MagicGames & Puzzles (01)


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16 of The Most BeautifulMathematical 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 Magic

6. Secret of Dies7. Traffic Jam Leap frogs Best Team-building game8. Tower of Hanoi Mathematical Recurrency9. Sum to 20 Game strategy 3 levels.10. Bai Qian Mai Bai Ji Problem of the 100 Fowls11. Han Xin Dian Bin Remainder Theorem

12. 9 Flips13. Consecutive Sum14. The Singapore Polytechnic Lockers15. Winners & the Chocolates16. $5 & $2 notes17. Who keep the Fish?


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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.
http://mind_reader.exe/http://mind_reader.exe/http://mind_reader.exe/http://mind_reader.exe/


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1

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 twonumbers, the forth number will be the

sum of second & third number, so on andso forth,The subsequence number will be the sum of

the previous two numbers, until you haveall the10 numbers

Now, ask the volunteers to add up all the10numbers.

(Someone will be able to tell you theSUMwell before theyhave completed the calculation. Why?)

2 Sum of 10 numbers Fibonacci Magic


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1

Think of any three digit number ABC

Rearrange the same three digits in any orderto 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 youranswer, and show me the remainingdigits. I will be able to tell the digit thatyou had removed.

Why? How?Three different digits

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

3 Magic Number 9

Cast out 9, Divisible by 9
http://mind_reader.exe/http://trunks.secondfoundation.org/files/psychic.swfhttp://trunks.secondfoundation.org/files/psychic.swfhttp://trunks.secondfoundation.org/files/psychic.swfhttp://trunks.secondfoundation.org/files/psychic.swfhttp://mind_reader.exe/http://mind_reader.exe/


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4. magic/puzzle

Trace the five shapesshown in the Figureon a sheet ofcardboard or stiffpaper, and cut them

out.Can you fit them

together to make the4 x 5 rectangleas shown in ?

Pieces may be turned overand placed with eitherside up.

Can you fit them together to

form a 4 x 5rectangle as shown?

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


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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 1112 13 14 15

24 25 26 27

28 29 30 31

Table D

16 17 18 1920 21 22 23

24 25 26 27

28 29 30 31

Table E

5. Magic Tables


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7. Traffic Jam - Fishing BoatLeap-Frog

Ten Men are fishing from a boat, five in thefront, five in the back, and there is one

empty seat in the middle. The five in frontare catching all the fish, so the five at theback want to change seats.

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

1. A man may move from his seat to and empty seatnext 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 manymoves is needed for the swap?


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

1891) constructed a puzzle with three pegsand seven rings of different sizes that couldslide onto the pegs.

Starting with all the rings in one peg in order by size,

the problem is to transfer the pile to another pegsubject to two conditions:

Rings are moved one by one, and no ring isever 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/
http://www.mathsnet.net/puzzles/hanoi/http://www.mathsnet.net/puzzles/hanoi/http://www.mathsnet.net/puzzles/hanoi/http://www.mathsnet.net/puzzles/hanoi/


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Select all the cards with 1 to 5

You are now having a pool of cards with 4sets 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 cardfrom the pool, and sum up the numbersof all the cards selected from bothplayers

Whoever gets the last card that the totalsum reaches 20 win the game.

Who will win? How?

9.


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A man paid exactly 100 dollars for 100chicken

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?

10Bai Qian Mai Bai Ji


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11Han Xin Dian Bing 1/21. Han Xin, an Han dynasty general, devised a

method to count the exact number of hissoldiers.

.

3. How did he do that?

What is the exact number of soldiers?


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Han Xin Dian Bing Solution

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

No

Divisor

D

Remainder X Remainder Multiplicationof

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


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Han Xin Dian Bing SolutionTwo Remainder Theorems: 1.Number X multiply by M, remainder also multiply by M2.Addition of Multiple of divisor, X + D x M, Remainder unchanged

Han Xin Dian Bing; the real question

NumberDivisor remainder X remainder Multiplication

of remainderFinal

value

N 5 1

N 6 5

N 7 4

N 11 10

Sum

LCM

N=


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abcdefghijkl

X 9

lkjihgfedcba

12. 9 Flips

What is the12digit numberabcdefghijkl ?

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 forshort that N is a 9-Flip

Find all 9-flips with 12 digits

Is it possible to say exactly how many 9-flips there are with precisely n

digits?


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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 consecutivesum? Old or even integers? average

2. Exactly How many solutions will it be? Ifthere 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 = ??


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At Singapore Polytechnic, there were 1,000 students and1,000 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 alongand 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,

Whichlockers 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 threeprize 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 plus1/3 of a bar,The Third winner received 2/3 of the New remainderplus 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?


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16. $5 & $ 2 notes

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

When $50 worth of $2 notes areconverted to $5 notes, the newration is 8 : 5.

How many $5 notes are there?

PSLE question


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Albert Einstein once posed a brain teaser that hepredicted only 2% of the world populationwould get.

FACTS1. There are 5 houses in 5 different colours

2. In each house lives a man with a differentnationality

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

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

17 Who keep the Fish?


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During the Foon Yew Maths Societygathering @ the auditorium

All members will shake hands witheach and everyone.

If, there were all together 36 hand-

shakes,

How many members are there?

36 Hand-Shakes


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20. The Handshaking party

On one Saturday,At the Foon Yew High

Alumni gathering @ City Square, only five marriedcouplesturn 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 samenumber of people.

With how many people does Mrs. Tan, thehostess shake hands?


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21.Ages of my Three ChildrenTwo friends, Chia How and Chong Heng, met at a Foon

Yew High gathering @ CITY Sqaure on Sat, after nothaving seen each other for many years.

As they talk,Chia How asked, How many children do youhave 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 needmore information to solve the problem.

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

With this additional information, Peter immediately foundthe answer.

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


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3 Mathematics Tutors are seated one behind another.

Another person showed them3 grey hats and 2 whitehats, 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 infront who could see no ones hat was able to respondcorrectly about his own hat.

How was this done ?

22. Mathematicians


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23.

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

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

There are two men ready to set out together.

Can the message be delivered and bothmen return to where they startedwithout going short of food?


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Libevents Mathmagic Slides