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Sagar Patil H13, IIT Bombay Logic Workshop

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H13, IIT Bombay. Logic Workshop . Sagar Patil. 3 Types of Puzzles. A) Computational Puzzles B) Ground Breaking Puzzles and Lateral thinking puzzles C) Exhaustion, elimination of cases type of puzzles. Usual Methods of Solving/Classification . - PowerPoint PPT Presentation

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Page 1: H13, IIT Bombay

Sagar Patil

H13, IIT BombayLogic Workshop

Page 2: H13, IIT Bombay

A) Computational PuzzlesB) Ground Breaking Puzzles and Lateral

thinking puzzlesC) Exhaustion, elimination of cases type of

puzzles

3 Types of Puzzles

Page 3: H13, IIT Bombay

Exhaustion: eliminating all possible cases and converging upon one final answer. Including Pigeon Hole Principle( Eg: A plane is coloured using 2 colours, prove that there are 2 points exactly one meters apart)

Contradiction; generate an apt contradictionContradicting, is an art. - Some great person

Mathematical InductionConstance, Parity; Strategy

Eg: 2 bishops of opposite colours can never kill each other etc

Geometry, spatial reasoningGroundbreaking thinking; Lateral thinking

Usual Methods of Solving/Classification

Page 4: H13, IIT Bombay

Puzzle 1:

There are 12 exactly identical coins, except one of them weighs different than others. Using a two scale weighing pan, find the minimum number of weightings required and the method by which one may find out the distinct coin aforementioned in that many number of weightings.

Lets dive in…

Page 5: H13, IIT Bombay

Let’s say that you have 25 horses, and you want to pick the fastest 3 horses out of those 25. In each race, only 5 horses can run at the same time because there are only 5 tracks. What is the minimum number of races required to find the 3 fastest horses without using a stopwatch?

Puzzle 2

Page 6: H13, IIT Bombay

What is/are the places(points) on earth wherefrom one can travel 20 Kms north, then 20 Kms west and then 20 Kms south to reach the point we were originally at?

Puzzle 3

Page 7: H13, IIT Bombay

Burning Rope A rope burns non-uniformly for exactly one hour. How do you measure 45 minutes, given two such ropes?

Puzzle 4

Page 8: H13, IIT Bombay

Puzzle 5: Chess Puzzle 1, 2

Page 9: H13, IIT Bombay

Chess Puzzles Continued…

Page 10: H13, IIT Bombay

Chess Puzzles… the last one

Page 11: H13, IIT Bombay

Three piles of rocks contain 1995, 1996, and 1997 rocks respectively. Two players in turn take any number of rocks from any one or two piles (they must take at least one rock from at least one pile). The player who takes the last rock wins. Find a strategy that allows one player to win regardless of how another one may play?

Puzzle 6

Page 12: H13, IIT Bombay

A pile contains 99 pebbles. Fred Flintstone and Barney Rubble in turn take pebbles from the pile: first Fred takes 1 pebble; then Barney takes one or two pebbles; then Fred takes 1 or 2 or 3 pebbles; then Barney takes 1 or 2 or 3 or 4 pebbles; etc. The player who takes the last pebble wins. Find a strategy that allows Fred or Barney to win regardless of how the other one may play.

Puzzle 7 (Winning Positions)

Page 13: H13, IIT Bombay

Given 3 barrels, an 8 litre barrel full of water, an empty 5 litre barrel, and an empty 3 litre barrel, describe the process of the consecutive pouring of water from barrel to barrel that ends up with 4 litres of water in the 8 litre barrel and 4 litres of water in the 5 litre barrel.(The barrels have no measuring mask on them, so all you can do is either empty a barrel completely into another one or fill a barrel to its capacity).

Puzzle 8

Page 14: H13, IIT Bombay

Every unit square of 1993*1993 chessboard contains a prince, a playing piece that can move horizontally or vertically to an adjacent square. Is it possible to have all princes make moves at once so that in the end, as in the beginning, every square of the board contains a prince?

Puzzle 9

Page 15: H13, IIT Bombay

Each of the 49 entries of a square 7*7 table is filled by an integer between 1 and 7, so that each column contains all the integers 1,2,3,4,5,6,7 and the table in symmetric w.r.t its diagonal D going from its upper left corner to its lower right corner. Prove that the diagonal D has all of the integers 1,2,3,4,5,6,7 on it.

Puzzle 10

Page 16: H13, IIT Bombay

Game: 2 players place coins of varying sizes (infinite number of coins of all sizes are available)on a circular table. The last player to place the coin wins. Find a winning strategy for player 1 or player 2.

Puzzle 11

Page 17: H13, IIT Bombay

Ant across the cube

Puzzle 12

Page 18: H13, IIT Bombay

Fastest path to the forest line and back home

Puzzle 13

Page 19: H13, IIT Bombay

2 guards, 2 doors(behind one door is a hungry tiger, behind another door is a very sexy girl who is crazy about the intellect of the 1st person coming through that door) - one always lies, one always speaks the truth, how to drive the truth out of them with our cunning IITian brains?

Puzzle 14

Page 20: H13, IIT Bombay

Grandpa's challenge (spatial reasoning)

Puzzle 15

Page 21: H13, IIT Bombay

John and his family members want to cross to the other side of the bridge at night. They have only one lamp which lasts for only 30 minutes. A maximum of only two persons can cross at one time, and they must have the lamp with them.

Each person walks at a different speed. John walks at a speed of 1 min, his brother jack walks at 3 min, his mother Julie walks at 6 min, his father Jeff walks at 8 min and his grandpa George walks at 12 min.

A pair must walk together at the rate of the slower person. How can John's family cross the bridge?

Puzzle 16: Family party:

Page 22: H13, IIT Bombay

The Naughty fly:

Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h. A fly starting out at the front of one train, flies towards the other at a speed of 75 km/h. Upon reaching the other train, the fly turns around and continues towards the first train. How many kilometers does the fly travel before getting squashed in the collision of the two trains?

Puzzle 17

Page 23: H13, IIT Bombay

http://www.folj.com/puzzles/

http://rohanrao.blogspot.com/

http://brainden.com

Mathematical Circles book; Dimitri Fomin, Sergey Jinkin, Ilia Itenberg

http://www.mathsisfun.com/puzzles

Resourses and links