H13, IIT Bombay

1. H13, IIT Bombay Logic Workshop SagarPatil

2. 3 Types of Puzzles • A) Computational Puzzles • B) Ground Breaking Puzzles and Lateral thinking puzzles • C) Exhaustion, elimination of cases type of puzzles

3. Usual Methods of Solving/Classification • 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 Induction • Constance, Parity; Strategy Eg: 2 bishops of opposite colours can never kill each other etc • Geometry, spatial reasoning • Groundbreaking thinking; Lateral thinking

4. Lets dive in… • 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.

5. Puzzle 2 • 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?

6. Puzzle 3 • 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?

7. Puzzle 4 • Burning Rope A rope burns non-uniformly for exactly one hour. How do you measure 45 minutes, given two such ropes?

8. Puzzle 5: Chess Puzzle 1, 2

9. Chess Puzzles Continued…

10. Chess Puzzles… the last one

11. Puzzle 6 • 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?

12. Puzzle 7 (Winning Positions) • 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.

13. Puzzle 8 • 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).

14. Puzzle 9 • 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?

15. Puzzle 10 • 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.

16. Puzzle 11 • 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.

17. Puzzle 12 • Ant across the cube

18. Puzzle 13 • Fastest path to the forest line and back home

19. Puzzle 14 • 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?

20. Puzzle 15 • Grandpa's challenge (spatial reasoning)

21. Puzzle 16: Family party: 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?

22. Puzzle 17 • 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?

23. Resourses and links • http://www.folj.com/puzzles/ • http://rohanrao.blogspot.com/ • http://brainden.com • MathematicalCircles book; Dimitri Fomin, SergeyJinkin, Ilia Itenberg • http://www.mathsisfun.com/puzzles