Thursday, January 24, 2019

Logic Puzzles with Solutions

Puzzle 1: How do you cut a circular cake into eight equal pieces in just 3 cuts?

Puzzle 2: You have a 3 liters and a 5 liters measuring jug. How are you going to get 4 liters from it?

Puzzle 3: You have 10 sets of 10 metal balls. You know the balls should weigh 10 g each. You know the balls in 1 set are exactly 1 g lighter. You are allowed to use an extremely accurate digital weighing scale only once. How do you determine which set of balls is lighter?

Puzzle 4: You have to fill the boxes with numbers from 1-8 by following below mentioned rules.
Rule 1: Predecessor and successor can’t be besides. Example if we take number 3 in any box, than neither side of 3 can have 2 or 4.
Rule 2: Predecessor and successor can’t be upside or downside. Example: if we take 3 in any box, then the box above can not have 2 or 4, similarly box below can not have 2 or 4.
Rule 3: Predecessor and successor can’t be diagonally either.

Puzzle 5: A Farmer had to cross a river, he had a Dog, a Chicken and some Corn. The Dog will bite the Chicken and the Chicken will eat the Corn if the Farmer is not around. The Farmer can only take 1 out of the 3 on the boat when crossing the river. How the Farmer can cross the river?

Puzzle 6: A dysfunctional family has to cross the river. On one side of the river are a Mother and 2 Daughters, Father and 2 Sons, the Maid and the Dog. There is a boat only big enough to hold 2 people (counting the dog as 1 person). Only the adults are capable of operating the boat. Everyone has to get to the other side, without anything bad happening.
Now the difficulties are : if the Dog is left with anyone and the Maid isn’t there to control him, he’ll bite. The Father can’t be left with any of the Daughters when the Mother isn’t there. Likewise, the Mother can’t be trusted alone with either of the Sons when the Father isn’t there.
Remember! only an adult can operate the boat, and the boat can’t drive itself.


Puzzle 7: A Cowboy need to cross the river with 4 Horses, he can only ride 1 and pull 1 when he cross. The Horses cross river at different speed, A require 1 minute, B require 2 minutes, C require 5 minutes and D require 10 minutes. The duration of the crossing will be the slowest Horse. If base on this logic, he cross with riding A and pulling the remaining Horses will be take 19 minutes in total as follows: A and B cross = 2 minutes, A come back = 1 minute, A and C cross = 5 minutes, A come back = 1 minute, A and D cross = 10 minutes. 2 + 1 + 5 + 1 + 10 = 19 minutes. But there is a way that he can complete the task at a shorter duration. Can you figure it out?

Puzzle 8: You got 8 eggs, 1 egg is spoil. The spoil egg is lighter than the other eggs. You can use a balancing scale only 2 times. Can you find out which egg is spoil?

Puzzle 9: You got 9 eggs, 1 egg is different. You do not know if the  egg is lighter or heavier than the other eggs. You can use a balancing scale only 3 times. Can you find out which egg is different?






Solution 1: Using 2 cuts to cut the cake into 4 equal pieces from the top, then using the 1 more cut to cut horizontally and you will get 8 equal pieces.


Solution 2: Fill the 5 liters jug. 
Pour 3 liters into the 3 liters jug with 2 liters remaining in the 5 liters jug. 
Empty the 3 liters jug. 
Pour the remaining 2 liters from the 5 liters jug into the 3 liters jug. Fill the 5 liters jug again. 
Pour 1 liter from the 5 liters jug into the 3 liters jug. 
Now the 5 liters jug will contains 4 liters.

Solution 3: Take 1 ball from the first set along with 2 balls from the second set and go on until you take 10 balls from the tenth set. If all the balls are 10 g you should get 550 g for 55 balls. If the weight is lighter by 1 g then it is the first set that is lighter, if the weight is lighter by 2 g then it is the second set which is lighter. By the reduce of weight you will be able to determine the set which is lighter.

Solution 4: 

Solution 5: The Farmer bring the Chicken cross the river.
The Farmer come back.
The Farmer bring the Dog cross the river.
The Farmer bring the Chicken back.
The Farmer bring the Corn cross the river.
The Farmer come back.
The Farmer bring the Chicken cross the river.

Solution 6: Maid and Dog cross first, and the Maid comes back.  
Maid and 1 Son cross, Maid and Dog come back. Father and another Son cross, Father comes back.
Mother and Father cross, Mother comes back.
Maid and Dog Cross, Father comes back.
Mother and Father cross, Mother comes back.
Mother and 1 Daughter cross, Maid and Dog come back.
Maid and another Daughter cross, Maid comes back.
Maid and Dog cross.

Solution 7: A and B cross = 2 minutes, A come back = 1 minute, C and D cross = 10 minutes, B come back = 2 minutes, A and B cross = 2 minutes. 2 + 1 + 10 + 2 + 2 = 17 minutes. 

Solution 8: Put 3 eggs on each side of the balance. 
If the scale tilt then the spoil egg is in the side which is higher. 
Take 2 eggs from the 3 eggs and put 1 egg on each side of the balance.
If the scale tilt then the spoil egg is in the side which is higher.

If the scale balance then the spoil egg is the remaining egg.
If the scale balance at first try then the spoil egg is in the remaining 2 eggs.
Take the 2 eggs and put 1 egg on each side of the balance.
The scale tilt with the spoil egg is on the side which is higher. 

Solution 9: Put 3 eggs on each side of the balance. 
If the scale tilt switch the remaining 3 eggs with the side which is higher.
If the scale still tilt, the egg is heavier and it is in the lower side.
If the scale balance, then the egg is lighter and it is in the set which you had just switch.
Take 2 eggs from the 3 eggs and put 1 egg on each side of the balance and you will be able to find the egg.

Wednesday, January 23, 2019

iChing Cipher


Recently had participate in another Treasure Hunt Event named Hunt The Hamster organize by Max Xu of Key Reply, he is a very talented guy who design a Bot software which give very smart reply to online query. The Hints draft by him for this event is really mind blowing and at a much higher level than the Hunt The Mouse Event organize by Sqkii. Although I didn't won the prize but I did enjoy the process of deciphering the hints together with other participants.

With the closure of the event, I realized that the Colour Number Matrix is not sufficient for more complicated kind of Treasure Hunt as it only able to give Number instead of Alphabet. I started to work on this Alphabet Cipher which had took me some time to draft the foundation. As I initially want to use Pyramid or Rubik Cube idea for the Cipher, but as I try out the idea I found that it is too complicated and not perfect as with the 26 Alphabets and 10 Numbers Digits I will only need 36 Variation. The 3 Sided Pyramid give 40 Variations and the Rubik Cube give 54 Variations, as I am thinking about the possibilities I realized that I will need a 6 Bit Binary System for the 36 Variations.

There are only 8 Bit Binary and Hex Code for the existing computer language, the only 6 Bit Binary that I had discover is the Braille Code which is use for the Blind People. So I decided to use the concept to draft my 6 Bit Binary Code and then later adapt the Code to the iChing which is having 64 Variations. As I only need 36 Variations there are 28 Variations in iChing which I never use, above is the Cipher Table.

Thursday, January 17, 2019

Treasure Hunt Concept

 Recently participated in Hunt The Mouse Event by Sqkii, after the event had ended I was inspired to create a better hints system for Treasure Hunt.

My Concept is base on Colour Number Matrix Table and it is related to Elements and Mythical Creatures. In the East is a Green Wood Unicorn named Jupiter. In the South is a Red Fire Phoenix named Mars. In the West is a Yellow Earth Lion named Saturn. In the North is a Blue Water Dragon named Mercury. In the Central is a White Metal Griffin named Venus.

The Colour Number Matrix Table start with Prime Number for Yellow Lion, then the Red Phoenix is using Multiple of 4. The Green Unicorn and Blue Dragon is random using a Table which is inspired by the Cicada Reproduction Cycle where it shift the cycle to Prime Number of 13 and 17 to avoid the Predator Reproduction Cycle of 4 Years Interval.

Cicada Reproduction Cycle


Yellow Lion Matrix using Prime Number

Red Phoenix Matrix using Multiple of 4 Interval



Green Unicorn Matrix


Blue Dragon Matrix


This Concept can be use for wide variety as it will give a 2 digits number which can be combine into a 6 digits Postal Code. Below is the Detail Explanation for the Treasure Hunt Concept.




East Green Wood Unicorn (CK Tang) Jupiter
Y9R23R6
 
Pasir Ris 51
(Red House) 191 Big Brass 506996 (R23)
(>Bukit Batok) B16B22R20
(Elias Playground) 625 Boat 510625 (Y9)
(>Sengkang) G13G24R4
 
Marine Parade 44
(White House) 37 Sea Breeze (R6)
Sea Breeze Lodge 449269
(>Pasir Ris) B12G17R25
 
Macpherson 37
(Dragon Playground) 53 Dragon 370053 (R23)
(>Toa Payoh) Y11Y1R11

 

South Red Fire Phoenix (Wheelock) Mars
Y9R23R20
 
Clifford Pier 04
(Merlion Park) 049213 (Y9)
(>Sentosa) G3G25B14
 
Mount Faber 09
(Merlion) 099448 (R23)
(>Clifford Pier) R2R24Y6
 
Sentosa 09
(Merlion) 099958 (R20)
(>Ang Mo Kio) R15Y1B3
(Dragon) 099702 (R23)
(>Toa Payoh) Y11R1R25

 
West Yellow Earth Lion (Taka) Saturn
Y9R23Y20
 
Bukit Batok 66
(Green House) 126B Generous
Hillview Mansion 669076 (Y9)
(>Punggol) B20B4Y20
(Keat Hong Mirage Playground)
818 Truck 681817 (R23)
(>Seletar) Y22Y23B20
 
Tiong Bahru 16
(Park Playground) 1 Train 168732 (Y20)
(>Bukit Batok) R18B3Y6

 

North Blue Water Dragon (Wisma) Mercury
Y9R23B19
 
Sembawang 75
(Park Playground) 117 Ship 759837 (R23)
(>Pasir Ris) G12G2B5 
(Canberra Park Playground)
325 Dinosaurs 750325 (Y9)
(>Woodlands) Y20R3B5
Woodlands 73
(Dinosaurs Playground) 81 Dinosaurs 730827 (Y9)
Fu Shan Garden
(>Toa Payoh) Y10R1B6
 
Seletar 79
(The Oval Playground) 2 Aeroplane 798386 (B19)
(>Tiong Bahru) R5G21R9
 
Sengkang 54
(Compassvale Cape Playground)
287A Ship 541287 (R23)
(>Sembawang) B18B25Y12
 
Punggol 82
(White House) 78 Treasure (B19)
Matilda House 822271
(>Marine Parade) R12R24G16


 
Central White Metal Griffin (Shaw) Venus
Y9R23R18
 
Ang Mo Kio 56
(Dragon Playground) 570 Dragon 560570 (Y9)
(>Toa Payoh) Y10R2R10
(Merlion Avenue 1) 560 Merlion 560218 (R18)
(>Mount Faber) G3G24R23
 
Toa Payoh 31
(Dragon Pillar) 91 Dragon 310096 (R18)
(>Whampoa Dragon Fountain) Y11R1R25
(Dragon Playground) 28 Dragon 310028 (R23)
(>Ang Mo Kio) R15Y3B16
(Dragon Playground) 240 Dragon 310240 (Y9)
(>Toa Payoh) Y11R1R7
(Dinosaurs Playground) Kim Keat Ville
27 Dinosaurs 310027 (R23)
(>Sembawang) B17Y2B5
 
Whampoa 32
(Dragon Fountain) 85 Dragon 310085 (R18)
(>Sentosa) G3Y25Y1

 

Orchard Road
CK Tang Green Wood Unicorn
238864 (WZJ119)
Wheelock Red Fire Phoenix
238880 (YGF9)
Taka Yellow Earth Lion
238873 (XS7)
Wisma Blue Water Dragon
238877 (DC80)
Shaw White Metal Griffin
238868 (XS23)
 


Simei 52 (Four Beauties Portraits)
(YGF9) 520107 (Red)
(XS7) 520116 (Yellow)
(XS23) 520123 (White)
(DC80) 520146 (Blue)
(WZJ119) 520226 (Green)


The participants will start the hunt first by choose one of the 4 Mythical Creatures, they will be given the Colour Matrix Card accordingly depend on which Mythical Creature they choose. They must team up with 3 other people who are holding different colour Matrix Card as they will need all 4 to decode the numbers. After they get the Matrix Card they will be given Hints on the one of the location which is in the area related to their Mythical Creature.

Once they arrive at the Location they will find a Code which will lead them to the next related location, they will also receive an additional partial code which will later lead them to an intermediate location in Orchard Road. For example if the participant choose Unicorn, he will be given the Code B12G17R25. The Code will indicate 12th Blue Number which is 50, 16th Green Number which is 62 and 25th Red Number which is 96. Combine the three set will give 506796 which is the Postal Code for Pasir Ris Red House.

At Pasir Ris Red House he will find another Code B16B22R20 which give 669076 which is the Postal Code for Green House in Bukit Batok which is also well known as Hill View Mansion. He will also find an Additional Partial Code of Y9 which is 23 for the Intermediate Location. 

If the player is smart enough he would be able to link the two locations and find the remaining 1 or 2 locations which is closely related to it. The White House in Punggol which is well known as Matilda House and another White House in Marine Parade which is well known as 37 Sea Breeze Lodge.

After they have collected the Postal Code of the Intermediate Location, they will find 5 Buildings Orchard Road which is related to the 5 Elements. Each Building will contain a Final Code which will lead them to the Final Location in Simei and the 5 Portrait of China Ancient Beauties will mark out an area which the Treasure is hidden.

There are many possibilities with this Concept, as the Number Digits can be use for Number Lock for Hints Box. Also can use IQ Question to test the Participants before they can obtain the Colour Matrix Card and the smarter one will be able to get more cards if they can solve more questions.