The Art and Science of Solving Puzzles

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Presentation transcript:

The Art and Science of Solving Puzzles Teasing your Brain to Think Critically The Art and Science of Solving Puzzles Pritam Bhattacharya (STCS, TIFR)

A Roadmap The River Crossing Problem The Mathematician’s Daughters Love in Kleptopia

The River Crossing Problem There are 3 cannibals & 3 missionaries, all standing on one bank of a river They need to get across a river There is a boat of capacity 2 If they are outnumbered, missionaries will be devoured by the cannibals How can all of them get to the other side of the river safely?

The River Crossing Problem (An Approach to a Solution) A Feasible Path Based Approach

The River Crossing Problem (Some Questions to Ponder) Is the solution we just saw the only possible solution? If not, how many other solutions exist? Among all possible solutions, did the solution we just saw use the least number of trips?

The Mathematician’s Daughters Mathematician has 3 daughters Product of their ages = 36 Sum of their ages = 13 Youngest daughter had a haircut What were the ages of the mathematician’s daughters? (Assume ages to be integers)

The Mathematician’s Daughters (The Path to the Solution) Product of their ages = 36 Sum of their ages = 13 Youngest daughter had a haircut (1,1,36) (1,6,6) (1,3,12) (1,4,9) (1,2,18) (3,3,4) (2,3,6) (2,2,9)

Love in Kleptopia How can Bob send the ring Kleptopia is a country full of thieves. Bob and Alice are citizens of Kleptopia. Bob plans to send an engagement ring to Alice. Needs to send it in a locked box to prevent theft. But then, Bob also needs to send the key to Alice. Key will get stolen if not sent in a locked box. How can Bob send the ring so that it does not get stolen and Alice can retrieve it?

BOB Alice

BOB Alice

BOB Alice

A Connection to Data Security Diffie-Hellman Key Exchange RSA Cryptosystem

The Hardness of Factorization Given 2 integers, it is easy to find their product. However, given an integer, it can be quite hard to find its prime factors, especially when it has large prime factors. For certain numbers with lots of digits, it can take even the fastest supercomputers a few years to come up with the prime factors of that integer. Can you tell me the prime factors of the number 667? Can you tell me the prime factors of the number 625? The security of the RSA cryptosystem is based on this very fact that factorization can be really hard.

THANK YOU! Take Home Message Solving logical puzzles can be loads of fun! They hone your critical thinking abilities. May lead to solution for a real-life problem. THANK YOU!